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A Multi-Index Generalized Derivative; Some Introductory Notes, M. Vivas-Cortez, L. M. Lugo, Juan E. Na ́Poles Valde ́S, M. E. Samei Nov 2022

A Multi-Index Generalized Derivative; Some Introductory Notes, M. Vivas-Cortez, L. M. Lugo, Juan E. Na ́Poles Valde ́S, M. E. Samei

Applied Mathematics & Information Sciences

In this work we present a generalized multi-index derivative, which contains as particular cases, with an index, several local derivatives known from the literature (both conformable and non-conformable). Obviously this new development contains many of the desirable properties of integer derivatives. It is worth noting that the multi-index differential operator departs from the classic single-order local derivatives, as in the case of the particular cases presented, which leads to an adequate and useful mathematical tool to generalize widely accepted results, with applications potentials to Physics, fundamental within mathematical simulation.

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Optimal Coordinated Search Problem For A Randomly Located Target, A. A. M. Teamah, A. A. Elbanna, H. A. Ismail Nov 2022

Optimal Coordinated Search Problem For A Randomly Located Target, A. A. M. Teamah, A. A. Elbanna, H. A. Ismail

Applied Mathematics & Information Sciences

The purpose of this paper is to study the coordinated search problem in which velocity of the searcher is a random variable. We are interested in finding a hole which randomly located on one of two disjoint oil pipelines or a cut in one of two lines of the power cable under sea surface. There are two searchers on every line that start the searching process from the origin of their line. In addition to calculating the expected value of the detection time, we derived the conditions which can minimize this expected value.:

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Optimization Task Scheduling Bee Colony Algorithm For Heterogeneous Cloud Computing Systems, Ahmed Y. Hamed, M. Kh. Elnahary, Hamdy H. El-Sayed Nov 2022

Optimization Task Scheduling Bee Colony Algorithm For Heterogeneous Cloud Computing Systems, Ahmed Y. Hamed, M. Kh. Elnahary, Hamdy H. El-Sayed

Applied Mathematics & Information Sciences

The primary purpose of the task scheduler is to assign tasks to available processors to produce a minimum Makespan without violating precedence constraints. In heterogeneous cloud computing resources, task assignments and schedules significantly impact system operation. In the experimental task scheduling algorithm, a different mapping of the process will result in a different maximum completion time of a batch of tasks (Makespan) on heterogeneous cloud computing resources. Thus, a scheduling algorithm has to define a schedule considering the precedence of child tasks depending on the resources required to reduce makespan. In this paper, we propose an Efficient Artificial Bee Colony …

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Decision Support Approach Based Rough Sets Theory To Investigate The Relationship Between Personality Traits And Drug User (Year-Based Definition), Abdelbaset A. Hares, H. A. Mohamed, Miad Abu Hawsah Nov 2022

Decision Support Approach Based Rough Sets Theory To Investigate The Relationship Between Personality Traits And Drug User (Year-Based Definition), Abdelbaset A. Hares, H. A. Mohamed, Miad Abu Hawsah

Applied Mathematics & Information Sciences

There is no doubt that the use of drugs has significant consequences for society, it introduces risk into the human life, increasing risk of poor health and greater earlier mortality and morbidity. The rapid growth of artificial intelligence and machine learning can provide useful tools for analyzing this problem; various methods have been given by researchers for increasing the prediction rate of drug users. This work proposes a decision support approach to investigate the relationship between drug user (year-based user definition) and personality traits. Psychologists approved the recent personality traits Five Factor Model (FFM) for understanding human individual differences. Two …

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Artificial Intelligence Security Model For Privacy Renitence In Big Data Analytics, S. Saravanan, M. Sivabalakrishnan, N. Duraimurugan, D. Divya Nov 2022

Artificial Intelligence Security Model For Privacy Renitence In Big Data Analytics, S. Saravanan, M. Sivabalakrishnan, N. Duraimurugan, D. Divya

Applied Mathematics & Information Sciences

The smart city uses Information and Communication Technologies (ICT) to build, run and sustain the environment, economic methods to overcome the growing problems of urbanization. Security, security, secrecy and validity have all been important factors in smart city applications, and they are also important in smart city infrastructure interfaces.Hence In this research, an Artificial Intelligence-Big Data Model (AIBM) was developed to enhance the data protection elements of information management interfaces in different smart city applications to address these concerns. A divergent evolutionary method has been implemented in AIBM to provide adequate security for the Secret Data Domain Controller for smart …

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Peristaltic Flow For A Mixture Of Blood And Gas Bubbles In The Vertical Inferior Mesenteric Vein, A. A. Elbendary, S. A. Mohammadein, F. A. El Hussiny, S. M. Elkholy, M. S. Ali Nov 2022

Peristaltic Flow For A Mixture Of Blood And Gas Bubbles In The Vertical Inferior Mesenteric Vein, A. A. Elbendary, S. A. Mohammadein, F. A. El Hussiny, S. M. Elkholy, M. S. Ali

Applied Mathematics & Information Sciences

In this paper, the viscous blood concentration and gas bubbles flow in the peristaltic vertical inferior mesenteric vein (IMV) are studied. The mass, concentration, and Navier-Stokes equations introduce the mathematical simulation of the current problem in the case of long wavelength and low Reynolds number with an analytical solution. The results introduced that the gradient pressure of a mixture of blood flow with gas bubbles performs larger values than that of blood without gas bubbles. Moreover, the blood concentration, velocity of blood and gas bubbles are very sensitive to the small change in blood density ratio, amplitude ratio, and modified …

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New Uniqueness Results For Fractional Differential Equations With A Caputo And Khalil Derivatives, Mahdi Rakah, Zoubir Dahmani, Abdelkader Senouci Nov 2022

New Uniqueness Results For Fractional Differential Equations With A Caputo And Khalil Derivatives, Mahdi Rakah, Zoubir Dahmani, Abdelkader Senouci

Applied Mathematics & Information Sciences

This paper in concerned with studying fractional differential problems involving two different derivatives. The first problem which involves the derivatives of Caputo is studied in its exisence and uniqueness of solutions. Then, an example is discussed to show the applicability of the result. In the second part, we use Khalil derivatives and the tanh numerical method to discuss traveling waves phenomena for a generalised partial differential equation. Some applications on beam equations are studied.

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On Orthogonal Special Class Of Caterpillars Squares, R. El-Shanawany, E. El-Kholy, T. Homoda, Z. Bakr Nov 2022

On Orthogonal Special Class Of Caterpillars Squares, R. El-Shanawany, E. El-Kholy, T. Homoda, Z. Bakr

Applied Mathematics & Information Sciences

Orthogonal Double Cover (ODC) is a set G of 2n subgraphs of a complete bipartite graph Kn,n of a graph G such that each edge in graph Kn,n appears once in both subgraphs of set G , and all subgraphs are isomorphic to graph G. we aim to construct two graph squares by a new engineering method that uses two induced starter functions to find the ODC of Kn,n. we also compose ODC from small to obtain a larger ODC. Starting from ODC F of Kq,q by qK2 we replace each point with n new points and each edge with …

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Dynamics Of A Stochastic And Deterministic Sviqrs Cholera Epidemic Model, Fikru S. Tessema, Boka K. Bole, Purnachandra R. Koya Nov 2022

Dynamics Of A Stochastic And Deterministic Sviqrs Cholera Epidemic Model, Fikru S. Tessema, Boka K. Bole, Purnachandra R. Koya

Applied Mathematics & Information Sciences

In the present research paper, deterministic and the corresponding stochastic mathematical models describing the dynamics of cholera epidemic are presented by incorporating vaccination. The total population size of the model is divided into five compartments namely Susceptible, Vaccinated, Infected, Quarantined for treatment and Recovered class. Initially, the cholera model is developed, and is determined by a deterministic approach. Since this deterministic approach is not considering either environmental factors or the randomness process of the dynamics, a corresponding stochastic approach has been introduced. The model equations of both deterministic and stochastic cases have been proved to be positive and also bounded. …

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Some Different Methods Via The Solution Of Volterra Integral Equation, M. A. Elsayed Nov 2022

Some Different Methods Via The Solution Of Volterra Integral Equation, M. A. Elsayed

Applied Mathematics & Information Sciences

In this paper, we establish, in a general case, the Volterra integral equation (VIE) from the initial value problems (IVPs). Also, some analytical and numerical methods are used to obtain the solution of VIE with a continuous kernel. In the numerical applications, the researcher based the Runge-Kutta and Trapezoid rules on the Simpson rule. This reference gives a fast convergence in the solution, a convergent error, and less than the previous traditional methods. Many numerical examples using Maple 18 are considered, and the estimated error, in each case, is computed. Keywords:

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On Study Nonlocal Integro Differential Equation Involving The The Caputo-Fabrizio Fractional Derivative And Q-Integral Of The Riemann Liouville Type, Amira Abd-Elall Ibrahim, Afaf A. S. Zaghrout, K. R. Raslan, Khalid K. Ali Nov 2022

On Study Nonlocal Integro Differential Equation Involving The The Caputo-Fabrizio Fractional Derivative And Q-Integral Of The Riemann Liouville Type, Amira Abd-Elall Ibrahim, Afaf A. S. Zaghrout, K. R. Raslan, Khalid K. Ali

Applied Mathematics & Information Sciences

In this work, the existence and uniqueness of a solution for the integro-differential equation that contains the Caputo-Fabrizio fractional derivative and the q-integral of the Riemann Liouville type will be investigated. The continuous dependence of the solution is studied. The Schauder fixed-point theorem is used to prove the existence of a solution to the addressed equation. In addition, we obtain a numerical solution for the proposed problem using a merge of finite difference with trapezoidal methods and a merge of cubic-b spline with trapezoidal methods. The definition of Caputo-Fabrizio fractional derivative and Riemann-Liouville q integral will be used. The finite …

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Graph Based Approach For Error-Detecting And Correcting Codes, R. El-Shanawany, S. A. El-Sheikh, S. A. El-Sheikh, S. R. Halawa, H. Shabana Nov 2022

Graph Based Approach For Error-Detecting And Correcting Codes, R. El-Shanawany, S. A. El-Sheikh, S. A. El-Sheikh, S. R. Halawa, H. Shabana

Applied Mathematics & Information Sciences

Combinatorial designs have properties that make them a significant tool for constructing good error detecting or correcting codes. In this paper, we use the fundamental properties of the incidence matrix of the graph designs (H , G, l ) to construct some efficient error detecting and correcting codes. In this manner, we consider H a regular graph, G a subgraph of H and l ≥ 2 to be an integer number. A (H,G,l) design is a collection of subgraphs G1,G2,··· ,Gb of H with each Gi ≃ G;i ∈ {1,2,···b}, every edge from H appears exactly l times in that …

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Linear Elliptic Control Problems Of Infinite Order With Pointwise State Constraints, Samira El-Tamimy Nov 2022

Linear Elliptic Control Problems Of Infinite Order With Pointwise State Constraints, Samira El-Tamimy

Applied Mathematics & Information Sciences

This paper deals with optimal control problems of systems governed by elliptic operator of infinite order with constraints on the state. Optimal control problem for linear elliptic equation is investigated. Existence of solution for elliptic control problem of infinite order with pointwise state constraints is obtained. Existence of optimal control of systems governed by elliptic operator of infinite order with pointwise state constraints is verified. Optimality conditions are given and reqularity of the optimal solution is investigated. Lagrange multipliers in the optimality condition of systems governed by elliptic operator of infinite order with pointwise state constraints are measures.

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The Cordiality Of Cone And Lemniscate Graphs, Ashraf Elrokh, Yasser Elmshtaye, Atef Abd El-Hay Nov 2022

The Cordiality Of Cone And Lemniscate Graphs, Ashraf Elrokh, Yasser Elmshtaye, Atef Abd El-Hay

Applied Mathematics & Information Sciences

A graph is said to be cordial if it has 0-1 labeling that satisfies certain conditions |v0 − v1 | ≤ 1 and |e0 − e1 | ≤ 1. In this paper we present necessary and sufficient conditions for cone and lemniscate graphs to be cordial.

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Peristaltic Transport Of Fractional Jeffrey Fluid In A Nonuniform Channel: Role Of Heat Transfer, H. S. Gafel Nov 2022

Peristaltic Transport Of Fractional Jeffrey Fluid In A Nonuniform Channel: Role Of Heat Transfer, H. S. Gafel

Applied Mathematics & Information Sciences

This articles goal is to explain how heat transfer affects the peristaltic movement of the fractional Jeffrey fluid over a permeable media in a non-uniform channel. The consequences of fractional viscoelastic properties of the generalized Jeffrey fluid are explored together with the effects of heat transfer, geometric features of the non-uniform channel, and peristaltic flow. There is a visual comparison between the two. By means of the suppositions of a long wavelength, the analytical solutions of the velocity, pressure gradient, and pressure rise are inspected. According to the data, the permeability, Grashof number, wave amplitude, heat source, thermal radiation, and …

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The Analytical And Simplest Resolution Of Linear Navier-Stokes Equations, S. A. Mohammadein, Ali. S. Ali, Maha. S. Ali Nov 2022

The Analytical And Simplest Resolution Of Linear Navier-Stokes Equations, S. A. Mohammadein, Ali. S. Ali, Maha. S. Ali

Applied Mathematics & Information Sciences

The nonlinear Navier-Stokes equations are converted to the linear diffusion equations by Mohammadein (Appl. Math. & Info. Sci. Lett. (2020). The analytical solutions of linear Navier-Stokes equations only are obtained. In this paper, the pressure gradient is redefined by using Bernoulli concept. The peristaltic incompressible viscous Newtonian fluid flow in a horizontal tube is described by Navier-Stokes equations. The stream function described the flow patterns (laminar, transit and turbulent) for different values of wave lengths. The linear and nonlinear Navier-Stokes equations are satisfied by the obtained analytical solutions based on pressure gradient definition.

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Estimation Of Sameera Distribution Parameters With Applications To Real Data, Loai Alzoubi, Mohammed Gharaibeha, Ahmad Al-Khazaleh, Mohammed Benrabia Nov 2022

Estimation Of Sameera Distribution Parameters With Applications To Real Data, Loai Alzoubi, Mohammed Gharaibeha, Ahmad Al-Khazaleh, Mohammed Benrabia

Applied Mathematics & Information Sciences

In this paper, a new two-parameter continuous distribution called Sameera distribution is proposed. Some statistical properties of this distribution are derived such as: moment-generating function, moments, and related measures, reliability analysis and associated functions. Also, the distribution of order statistics and the quantile function are presented. The Shannon, Re ́nyi, and Tsallis entropies are derived. The methods of maximum likelihood estimation, ordinary and weighted least squares, Anderson-Darling, Cramer-Von Mises, and maximum product spacing are used to estimate the distribution parameters. A simulation study is performed to investigate the performance of these methods. Real data applications show that the proposed distribution …

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Best Proximity Point Of Generalized (F − Τ )-Proximal Non-Self Contractions In Generalized Metric Spaces, Abdelkarim Kari, Hasanen A. Hammad, Adil Baiz, Mouline Jamal Nov 2022

Best Proximity Point Of Generalized (F − Τ )-Proximal Non-Self Contractions In Generalized Metric Spaces, Abdelkarim Kari, Hasanen A. Hammad, Adil Baiz, Mouline Jamal

Applied Mathematics & Information Sciences

In this manuscript, we introduce the idea of generalized (F,τ)-proximal contraction and prove new best proximity results for these contractions in the context of a generalized metric space. Our findings extend and generalize a number of previous results from the literature. Also, We present an example to illustrate the applicability of our results. Keywords:

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Numerical Solution Via A Singular Mixed Integral Equation In (2+1) Dimensional, A. R. Jan Nov 2022

Numerical Solution Via A Singular Mixed Integral Equation In (2+1) Dimensional, A. R. Jan

Applied Mathematics & Information Sciences

In this paper, under certain conditions, the unique solution of a mixed integral equation (MIE) with a singular kernel in position and a continuous kernel in time, in ( 2+1) dimensional is discussed and obtained in the space L2([a,b]×[c,d])×C[0,T],T < 1. After using a separation technique method, and Product Nystrom Method (PNM), we have a linear algebraic system (LAS) in two- dimensional with time coefficients. The convergence of the unique solution of the LAS is studied. In the end, and with the aid of Maple 18, many applications when a singular term of position kernel takes a logarithmic form and Carleman function are solved numerically. Moreover, the error is computed.

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Optimization Task Scheduling Bee Colony Algorithm For Heterogeneous Cloud Computing Systems, Ahmed Y. Hamed, M. Kh. Elnahary, Hamdy H. El-Sayed Nov 2022

Optimization Task Scheduling Bee Colony Algorithm For Heterogeneous Cloud Computing Systems, Ahmed Y. Hamed, M. Kh. Elnahary, Hamdy H. El-Sayed

Applied Mathematics & Information Sciences

The primary purpose of the task scheduler is to assign tasks to available processors to produce a minimum Makespan without violating precedence constraints. In heterogeneous cloud computing resources, task assignments and schedules significantly impact system operation. In the experimental task scheduling algorithm, a different mapping of the process will result in a different maximum completion time of a batch of tasks (Makespan) on heterogeneous cloud computing resources. Thus, a scheduling algorithm has to define a schedule considering the precedence of child tasks depending on the resources required to reduce makespan. In this paper, we propose an Efficient Artificial Bee Colony …

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Anti-Phishing Tools: State Of The Art And Detection Efficiencies, M. F. Alghenaim, N. A. Abu Bakar, F. Abdul Rahim Nov 2022

Anti-Phishing Tools: State Of The Art And Detection Efficiencies, M. F. Alghenaim, N. A. Abu Bakar, F. Abdul Rahim

Applied Mathematics & Information Sciences

A phishing attack is a process of obtaining a customers private data, whether by using phishing emails or fake websites. With every new development on the Internet, the attackers means of phishing attacks develop, requiring more powerful phishing tools to counter these attacks. The Internet has become an essential part of the personal and social life of the public and governments, institutions, and companies all over the world. This means that Internet users need tools to protect against phishing attack types and web risks, which may cause personal, institutional, financial, and informational damage. Hence, this study reviews anti-phishing attack tools …

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Peristaltic Flow For A Mixture Of Blood And Gas Bubbles In The Vertical Inferior Mesenteric Vein, A. A. Elbendary, S. A. Mohammadein, F. A. El Hussiny, S. M. Elkholy, M. S. Ali Nov 2022

Peristaltic Flow For A Mixture Of Blood And Gas Bubbles In The Vertical Inferior Mesenteric Vein, A. A. Elbendary, S. A. Mohammadein, F. A. El Hussiny, S. M. Elkholy, M. S. Ali

Applied Mathematics & Information Sciences

In this paper, the viscous blood concentration and gas bubbles flow in the peristaltic vertical inferior mesenteric vein (IMV) are studied. The mass, concentration, and Navier-Stokes equations introduce the mathematical simulation of the current problem in the case of long wavelength and low Reynolds number with an analytical solution. The results introduced that the gradient pressure of a mixture of blood flow with gas bubbles performs larger values than that of blood without gas bubbles. Moreover, the blood concentration, velocity of blood and gas bubbles are very sensitive to the small change in blood density ratio, amplitude ratio, and modified …

Go to article

New Uniqueness Results For Fractional Differential Equations With A Caputo And Khalil Derivatives, Mahdi Rakah, Zoubir Dahmani, Abdelkader Senouci Nov 2022

New Uniqueness Results For Fractional Differential Equations With A Caputo And Khalil Derivatives, Mahdi Rakah, Zoubir Dahmani, Abdelkader Senouci

Applied Mathematics & Information Sciences

This paper in concerned with studying fractional differential problems involving two different derivatives. The first problem which involves the derivatives of Caputo is studied in its exisence and uniqueness of solutions. Then, an example is discussed to show the applicability of the result. In the second part, we use Khalil derivatives and the tanh numerical method to discuss traveling waves phenomena for a generalised partial differential equation. Some applications on beam equations are studied.

Go to article

On Orthogonal Special Class Of Caterpillars Squares, R. El-Shanawany, E. El-Kholy, T. Homoda, Z. Bakr Nov 2022

On Orthogonal Special Class Of Caterpillars Squares, R. El-Shanawany, E. El-Kholy, T. Homoda, Z. Bakr

Applied Mathematics & Information Sciences

Orthogonal Double Cover (ODC) is a set G of 2n subgraphs of a complete bipartite graph Kn,n of a graph G such that each edge in graph Kn,n appears once in both subgraphs of set G , and all subgraphs are isomorphic to graph G. we aim to construct two graph squares by a new engineering method that uses two induced starter functions to find the ODC of Kn,n. we also compose ODC from small to obtain a larger ODC. Starting from ODC F of Kq,q by qK2 we replace each point with n new points and each edge with …

Go to article

Dynamics Of A Stochastic And Deterministic Sviqrs Cholera Epidemic Model, Fikru S. Tessema, Boka K. Bole, Purnachandra R. Koya Nov 2022

Dynamics Of A Stochastic And Deterministic Sviqrs Cholera Epidemic Model, Fikru S. Tessema, Boka K. Bole, Purnachandra R. Koya

Applied Mathematics & Information Sciences

In the present research paper, deterministic and the corresponding stochastic mathematical models describing the dynamics of cholera epidemic are presented by incorporating vaccination. The total population size of the model is divided into five compartments namely Susceptible, Vaccinated, Infected, Quarantined for treatment and Recovered class. Initially, the cholera model is developed, and is determined by a deterministic approach. Since this deterministic approach is not considering either environmental factors or the randomness process of the dynamics, a corresponding stochastic approach has been introduced. The model equations of both deterministic and stochastic cases have been proved to be positive and also bounded. …

Go to article

Some Different Methods Via The Solution Of Volterra Integral Equation, M. A. Elsayed Nov 2022

Some Different Methods Via The Solution Of Volterra Integral Equation, M. A. Elsayed

Applied Mathematics & Information Sciences

In this paper, we establish, in a general case, the Volterra integral equation (VIE) from the initial value problems (IVPs). Also, some analytical and numerical methods are used to obtain the solution of VIE with a continuous kernel. In the numerical applications, the researcher based the Runge-Kutta and Trapezoid rules on the Simpson rule. This reference gives a fast convergence in the solution, a convergent error, and less than the previous traditional methods. Many numerical examples using Maple 18 are considered, and the estimated error, in each case, is computed. Keywords:

Go to article

On Study Nonlocal Integro Differential Equation Involving The The Caputo-Fabrizio Fractional Derivative And Q-Integral Of The Riemann Liouville Type, Amira Abd-Elall Ibrahim, Afaf A. S. Zaghrout, K. R. Raslan, Khalid K. Ali Nov 2022

On Study Nonlocal Integro Differential Equation Involving The The Caputo-Fabrizio Fractional Derivative And Q-Integral Of The Riemann Liouville Type, Amira Abd-Elall Ibrahim, Afaf A. S. Zaghrout, K. R. Raslan, Khalid K. Ali

Applied Mathematics & Information Sciences

In this work, the existence and uniqueness of a solution for the integro-differential equation that contains the Caputo-Fabrizio fractional derivative and the q-integral of the Riemann Liouville type will be investigated. The continuous dependence of the solution is studied. The Schauder fixed-point theorem is used to prove the existence of a solution to the addressed equation. In addition, we obtain a numerical solution for the proposed problem using a merge of finite difference with trapezoidal methods and a merge of cubic-b spline with trapezoidal methods. The definition of Caputo-Fabrizio fractional derivative and Riemann-Liouville q integral will be used. The finite …

Go to article

Graph Based Approach For Error-Detecting And Correcting Codes, R. El-Shanawany, S. A. El-Sheikh, S. A. El-Sheikh, S. R. Halawa, H. Shabana Nov 2022

Graph Based Approach For Error-Detecting And Correcting Codes, R. El-Shanawany, S. A. El-Sheikh, S. A. El-Sheikh, S. R. Halawa, H. Shabana

Applied Mathematics & Information Sciences

Combinatorial designs have properties that make them a significant tool for constructing good error detecting or correcting codes. In this paper, we use the fundamental properties of the incidence matrix of the graph designs (H , G, l ) to construct some efficient error detecting and correcting codes. In this manner, we consider H a regular graph, G a subgraph of H and l ≥ 2 to be an integer number. A (H,G,l) design is a collection of subgraphs G1,G2,··· ,Gb of H with each Gi ≃ G;i ∈ {1,2,···b}, every edge from H appears exactly l times in that …

Go to article

Linear Elliptic Control Problems Of Infinite Order With Pointwise State Constraints, Samira El-Tamimy Nov 2022

Linear Elliptic Control Problems Of Infinite Order With Pointwise State Constraints, Samira El-Tamimy

Applied Mathematics & Information Sciences

This paper deals with optimal control problems of systems governed by elliptic operator of infinite order with constraints on the state. Optimal control problem for linear elliptic equation is investigated. Existence of solution for elliptic control problem of infinite order with pointwise state constraints is obtained. Existence of optimal control of systems governed by elliptic operator of infinite order with pointwise state constraints is verified. Optimality conditions are given and reqularity of the optimal solution is investigated. Lagrange multipliers in the optimality condition of systems governed by elliptic operator of infinite order with pointwise state constraints are measures.

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Hadamard-Feje ́R Type Inequalities Related To Φm−Convex Function, Miguel Vivas Cortez, Muhammad Shoib Saleem, Razi Ur Rehman Nov 2022

Hadamard-Feje ́R Type Inequalities Related To Φm−Convex Function, Miguel Vivas Cortez, Muhammad Shoib Saleem, Razi Ur Rehman

Applied Mathematics & Information Sciences

We will bring up a new generalization φm−convex function for the convex function. We give some basic properties for this notion. Furthermore, we set down proofs of Hermite-Hadamard type and Hermite-Hadamard-Feje ́r type integral inequalities for this notion.

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