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Articles 91 - 120 of 138
Full-Text Articles in Analysis
Numerical Solution Of Linear Fredholm Integro-Differential Equations By Non-Standard Finite Difference Method, Pramod K. Pandey
Numerical Solution Of Linear Fredholm Integro-Differential Equations By Non-Standard Finite Difference Method, Pramod K. Pandey
Applications and Applied Mathematics: An International Journal (AAM)
In this article we consider a non-standard finite difference method for numerical solution of linear Fredholm integro-differential equations. The non-standard finite difference method and the repeated / composite trapezoidal quadrature method are used to transform the Fredholm integro-differential equation into a system of non-linear algebraic equations. The numerical experiments on some linear model problems show the simplicity and efficiency of the proposed method. It is observed from the numerical experiments that our method is convergent and second order accurate.
On The Growth Of Solutions Of The Generalized Axially Symmetric, Reduced Wave Equation In (N + 1) Variables, Devendra Kumar
On The Growth Of Solutions Of The Generalized Axially Symmetric, Reduced Wave Equation In (N + 1) Variables, Devendra Kumar
Applications and Applied Mathematics: An International Journal (AAM)
In this paper we have investigated the growth properties of solutions of the generalized axially symmetric, reduced wave equation in (n + 1) variables. Results analogus to those for order and type found in the theory of entire functions of several complex variables, of solutions, in terms of their expansion coefficients have been obtained. Our study is essential to a detailed understanding of the scattering of waves by central potentials and may be applied for generalized (n + 2)dimensional problems of potential scattering in quantum mechanics.
The Fuzzy Over-Relaxed Proximal Point Iterative Scheme For Generalized Variational Inclusion With Fuzzy Mappings, Rais Ahmad, Mijanur Rahaman, Haider A. Rizvi
The Fuzzy Over-Relaxed Proximal Point Iterative Scheme For Generalized Variational Inclusion With Fuzzy Mappings, Rais Ahmad, Mijanur Rahaman, Haider A. Rizvi
Applications and Applied Mathematics: An International Journal (AAM)
This paper deals with the introduction of a fuzzy over-relaxed proximal point iterative scheme based on H(-, -)-cocoercivity framework for solving a generalized variational inclusion problem with fuzzy mappings. The resolvent operator technique is used to approximate the solution of generalized variational inclusion problem with fuzzy mappings and convergence of the iterative sequences generated by the iterative scheme is discussed. Our results can be treated as refinement of many previously-known results.
The Shifted Jacobi Polynomial Integral Operational Matrix For Solving Riccati Differential Equation Of Fractional Order, A. Neamaty, B. Agheli, R. Darzi
The Shifted Jacobi Polynomial Integral Operational Matrix For Solving Riccati Differential Equation Of Fractional Order, A. Neamaty, B. Agheli, R. Darzi
Applications and Applied Mathematics: An International Journal (AAM)
In this article, we have applied Jacobi polynomial to solve Riccati differential equation of fractional order. To do so, we have presented a general formula for the Jacobi operational matrix of fractional integral operator. Using the Tau method, the solution of this problem reduces to the solution of a system of algebraic equations. The numerical results for the examples presented in this paper demonstrate the efficiency of the present method.
Local Fractional Variational Iteration Method For Solving Nonlinear Partial Differential Equations Within Local Fractional Operators, Hossein Jafari, Hassan K. Jassim
Local Fractional Variational Iteration Method For Solving Nonlinear Partial Differential Equations Within Local Fractional Operators, Hossein Jafari, Hassan K. Jassim
Applications and Applied Mathematics: An International Journal (AAM)
In this article, the local fractional variational iteration method is proposed to solve nonlinear partial differential equations within local fractional derivative operators. To illustrate the ability and reliability of the method, some examples are illustrated. A comparison between local fractional variational iteration method with the other numerical methods is given, revealing that the proposed method is capable of solving effectively a large number of nonlinear differential equations with high accuracy. In addition, we show that local fractional variational iteration method is able to solve a large class of nonlinear problems involving local fractional operators effectively, more easily and accurately, and …
Existence Of Mild Solutions For Semilinear Impulsive Functional Mixed Integro-Differential Equations With Nonlocal Conditions, Kamalendra Kumar, Rakesh Kumar
Existence Of Mild Solutions For Semilinear Impulsive Functional Mixed Integro-Differential Equations With Nonlocal Conditions, Kamalendra Kumar, Rakesh Kumar
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we prove the existence, uniqueness and continuous dependence of initial data on mild solutions of first order semilinear functional impulsive mixed integro-differential equations with nonlocal condition in general Banach spaces. The results are obtained by using the semigroup theory and Banach contraction theorem.
Reichenbach Fuzzy Set Of Transitivity, Samina Ashraf, Muhammad A. Javed
Reichenbach Fuzzy Set Of Transitivity, Samina Ashraf, Muhammad A. Javed
Applications and Applied Mathematics: An International Journal (AAM)
Fuzzy implicators are the basic ingredients of many applications. So it becomes essential to study the various features of an implicator before implementing it in any practical application. This paper discusses the properties of transitivity of a fuzzy relation on a given universe and measure of fuzzy transitivity defined in terms of the Reichenbach fuzzy implicator which is an s-implicator.
Application Of The Extended G'/G-Expansion Method To The Improved Eckhaus Equation, Nasir Taghizadeh, Seyyedeh R. Moosavi Noori, Seyyedeh B. Moosavi Noori
Application Of The Extended G'/G-Expansion Method To The Improved Eckhaus Equation, Nasir Taghizadeh, Seyyedeh R. Moosavi Noori, Seyyedeh B. Moosavi Noori
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, the extended (G'/G)-expansion method is used to seek more general exact solutions of the improved Eckhaus equation and the (2+1)-dimensional improved Eckhaus equation. As a result, hyperbolic function solutions, trigonometric function solutions and rational function solutions with free parameters are obtained. When the parameters are taken as special values the solitary wave solutions are also derived from the traveling wave solutions. Moreover, it is shown that the proposed method is direct, effective and can be used for many other nonlinear evolution equations in mathematical physics.
A New Adjustment Of Laplace Transform For Fractional Bloch Equation In Nmr Flow, Sunil Kumar, Devendra Kumar, U. S. Mahabaleshwar
A New Adjustment Of Laplace Transform For Fractional Bloch Equation In Nmr Flow, Sunil Kumar, Devendra Kumar, U. S. Mahabaleshwar
Applications and Applied Mathematics: An International Journal (AAM)
This work purpose suggest a new analytical technique called the fractional homotopy analysis transform method (FHATM) for solving time fractional Bloch NMR (nuclear magnetic resonance) flow equations, which are a set of macroscopic equations that are used for modeling nuclear magnetization as a function of time. The true beauty of this article is the coupling of the homotopy analysis method and the Laplace transform method for systems of fractional differential equations. The solutions obtained by the proposed method indicate that the approach is easy to implement and computationally very attractive.
On Some Hadamard-Type Inequalıtıes For (R,M) -Convex Functıons, M. E. Özdemir, Erhan Set, Ahmet O. Akdemir
On Some Hadamard-Type Inequalıtıes For (R,M) -Convex Functıons, M. E. Özdemir, Erhan Set, Ahmet O. Akdemir
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we define a new class of convex functions which is called (r,m) - convex functions. We also prove some Hadamard's type inequalities based on this new definition.
Reliable Study Of Nonhomogeneous Bbm Equation With Time-Dependent Coefficients By The Modified Sine-Cosine Method, Aminah Qawasmeh, Marwan Alquran
Reliable Study Of Nonhomogeneous Bbm Equation With Time-Dependent Coefficients By The Modified Sine-Cosine Method, Aminah Qawasmeh, Marwan Alquran
Applications and Applied Mathematics: An International Journal (AAM)
The modified sine-cosine method is an efficient and powerful mathematical tool in finding exact traveling wave solutions to nonlinear partial differential equations (NLPDEs) with time-dependent coefficients. In this paper, the proposed approach is applied to study a nonhomogeneous generalized form of Benjamin-Bona-Mahony (BBM) equation with time-dependent coefficients. Explicit traveling wave solutions of the equation are obtained under certain constraints on the coefficient functions.
Existence Of Solutions For Multi-Points Fractional Evolution Equations, Soumia Belarbi, Zoubir Dahmani
Existence Of Solutions For Multi-Points Fractional Evolution Equations, Soumia Belarbi, Zoubir Dahmani
Applications and Applied Mathematics: An International Journal (AAM)
In this paper we study an impulsive fractional evolution equation with nonlinear boundary conditions. Sufficient conditions for the existence and uniqueness of solutions are established. To illustrate our results, an example is presented.
Certain Fractional Integral Operators And The Generalized Incomplete Hypergeometric Functions, H. M. Srivastava, Praveen Agarwal
Certain Fractional Integral Operators And The Generalized Incomplete Hypergeometric Functions, H. M. Srivastava, Praveen Agarwal
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we apply a certain general pair of operators of fractional integration involving Appell’s function F3 in their kernel to the generalized incomplete hypergeometric functions pΓq[z] and pɣq [z], which were introduced and studied systematically by Srivastava et al. in the year 2012. Some interesting special cases and consequences of our main results are also considered.
A New Approach To The Numerical Solution Of Fractional Order Optimal Control Problems, T. Akbarian, M. Keyanpour
A New Approach To The Numerical Solution Of Fractional Order Optimal Control Problems, T. Akbarian, M. Keyanpour
Applications and Applied Mathematics: An International Journal (AAM)
In this article, a new numerical method is proposed for solving a class of fractional order optimal control problems. The fractional derivative is considered in the Caputo sense. This approach is based on a combination of the perturbation homotopy and parameterization methods. The control function u(t) is approximated by polynomial functions with unknown coefficients. This method converts the fractional order optimal control problem to an optimization problem. Numerical results are included to demonstrate the validity and applicability of the method.
Generalized Fractional Integral Of The Product Of Two Aleph-Functions, R. K. Saxena, J. Ram, D. Kumar
Generalized Fractional Integral Of The Product Of Two Aleph-Functions, R. K. Saxena, J. Ram, D. Kumar
Applications and Applied Mathematics: An International Journal (AAM)
This paper is devoted to the study and develops the generalized fractional integral operators for a new special function, which is called Aleph-function. The considered generalized fractional integration operators contain the Appell hypergeometric function F3 as a kernel. We establish two results of the product of two Aleph-functions involving Saigo-Maeda operators. On account of the general nature of the Saigo-Maeda operators and the Aleph-function, some results involving Saigo, Riemann-Liouville and Erdélyi-Kober integral operators are obtained as special cases of the main result.
A Subdivision-Regularization Framework For Preventing Over Fitting Of Data By A Model, Ghulam Mustafa, Abdul Ghaffar, Muhammad Aslam
A Subdivision-Regularization Framework For Preventing Over Fitting Of Data By A Model, Ghulam Mustafa, Abdul Ghaffar, Muhammad Aslam
Applications and Applied Mathematics: An International Journal (AAM)
First, we explore the properties of families of odd-point odd-ary parametric approximating subdivision schemes. Then we fine-tune the parameters involved in the family of schemes to maximize the smoothness of the limit curve and error bounds for the distance between the limit curve and the kth level control polygon. After that, we present the subdivision-regularization framework for preventing over fitting of data by model. Demonstration shows that the proposed unified frame work can work well for both noise removal and overfitting prevention in subdivision as well as regularization.
Further Results On Fractional Calculus Of Saigo Operators, Praveen Agarwal
Further Results On Fractional Calculus Of Saigo Operators, Praveen Agarwal
Applications and Applied Mathematics: An International Journal (AAM)
A significantly large number of earlier works on the subject of fractional calculus give interesting account of the theory and applications of fractional calculus operators in many different areas of mathematical analysis (such as ordinary and partial differential equations, integral equations, special functions, summation of series, et cetera). The main object of the present paper is to study and develop the Saigo operators. First, we establish two results that give the image of the product of multivariable H-function and a general class of polynomials in Saigo operators. On account of the general nature of the Saigo operators, multivariable H-function and …
Two Reliable Methods For Solving The Modified Improved Kadomtsev-Petviashvili Equation, N. Taghizadeh, S. R. Moosavi Noori
Two Reliable Methods For Solving The Modified Improved Kadomtsev-Petviashvili Equation, N. Taghizadeh, S. R. Moosavi Noori
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, the tanh-coth method and the extended (G'/G)-expansion method are used to construct exact solutions of the nonlinear Modified Improved Kadomtsev-Petviashvili (MIKP) equation. These methods transform nonlinear partial differential equation to ordinary differential equation and can be applied to nonintegrable equation as well as integrable ones. It has been shown that the two methods are direct, effective and can be used for many other nonlinear evolution equations in mathematical physics.
Applying Differential Transform Method To Nonlinear Partial Differential Equations: A Modified Approach, Marwan T. Alquran
Applying Differential Transform Method To Nonlinear Partial Differential Equations: A Modified Approach, Marwan T. Alquran
Applications and Applied Mathematics: An International Journal (AAM)
This paper proposes another use of the Differential transform method (DTM) in obtaining approximate solutions to nonlinear partial differential equations (PDEs). The idea here is that a PDE can be converted to an ordinary differential equation (ODE) upon using a wave variable, then applying the DTM to the resulting ODE. Three equations, namely, Benjamin-Bona-Mahony (BBM), Cahn-Hilliard equation and Gardner equation are considered in this study. The proposed method reduces the size of the numerical computations and use less rules than the usual DTM method used for multi-dimensional PDEs. The results show that this new approach gives very accurate solutions.
Coding Theorems On A Non-Additive Generalized Entropy Of Havrda-Charvat And Tsallis, Satish Kumar, Arun Choudhary
Coding Theorems On A Non-Additive Generalized Entropy Of Havrda-Charvat And Tsallis, Satish Kumar, Arun Choudhary
Applications and Applied Mathematics: An International Journal (AAM)
A new measure Lβα, called average code word length of order α and type β is defined and its relationship with a generalized information measure of order α and type β is discussed. Using Lβα , some coding theorems are proved.
Geometric Programming Subject To System Of Fuzzy Relation Inequalities, Elyas Shivanian, Mahdi Keshtkar, Esmaile Khorram
Geometric Programming Subject To System Of Fuzzy Relation Inequalities, Elyas Shivanian, Mahdi Keshtkar, Esmaile Khorram
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, an optimization model with geometric objective function is presented. Geometric programming is widely used; many objective functions in optimization problems can be analyzed by geometric programming. We often encounter these in resource allocation and structure optimization and technology management, etc. On the other hand, fuzzy relation equalities and inequalities are also used in many areas. We here present a geometric programming model with a monomial objective function subject to the fuzzy relation inequality constraints with maxproduct composition. Simplification operations have been given to accelerate the resolution of the problem by removing the components having no effect on …
Fractional Integrals And Derivatives For Sumudu Transform On Distribution Spaces, Deshna Loonker, P. K. Banerji
Fractional Integrals And Derivatives For Sumudu Transform On Distribution Spaces, Deshna Loonker, P. K. Banerji
Applications and Applied Mathematics: An International Journal (AAM)
We propose, in the present paper, the investigation of the Sumudu transformation for certain distribution spaces with regard to the fractional integral and differential operators of the transform. This paper is organized in two sections, first of which gives an abriged text on fractional operators and the Sumudu transform (which is less discussed and reserached). Basic concept in analysing the investigation is initiated by the fact that the Riemann-Liouville fractional integral can be expressed as one of the appropriate forms of the Abel integral equation, which is the second section of this paper.
Two Numerical Algorithms For Solving A Partial Integro-Differential Equation With A Weakly Singular Kernel, Jeong-Mi Yoon, Shishen Xie, Volodymyr Hrynkiv
Two Numerical Algorithms For Solving A Partial Integro-Differential Equation With A Weakly Singular Kernel, Jeong-Mi Yoon, Shishen Xie, Volodymyr Hrynkiv
Applications and Applied Mathematics: An International Journal (AAM)
Two numerical algorithms based on variational iteration and decomposition methods are developed to solve a linear partial integro-differential equation with a weakly singular kernel arising from viscoelasticity. In addition, analytic solution is re-derived by using the variational iteration method and decomposition method.
A Novel Algorithm To Forecast Enrollment Based On Fuzzy Time Series, Haneen T. Jasim, Abdul G. Jasim Salim, Kais I. Ibraheem
A Novel Algorithm To Forecast Enrollment Based On Fuzzy Time Series, Haneen T. Jasim, Abdul G. Jasim Salim, Kais I. Ibraheem
Applications and Applied Mathematics: An International Journal (AAM)
In this paper we propose a new method to forecast enrollments based on fuzzy time series. The proposed method belongs to the first order and time-variant methods. Historical enrollments of the University of Alabama from year 1948 to 2009 are used in this study to illustrate the forecasting process. By comparing the proposed method with other methods we will show that the proposed method has a higher accuracy rate for forecasting enrollments than the existing methods.
Exact Solutions Of The Generalized Benjamin Equation And (3 + 1)- Dimensional Gkp Equation By The Extended Tanh Method, N. Taghizadeh, M. Mirzazadeh, S. R. Moosavi Noori
Exact Solutions Of The Generalized Benjamin Equation And (3 + 1)- Dimensional Gkp Equation By The Extended Tanh Method, N. Taghizadeh, M. Mirzazadeh, S. R. Moosavi Noori
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, the extended tanh method is used to construct exact solutions of the generalized Benjamin and (3 + 1)-dimensional gKP equation. This method is shown to be an efficient method for obtaining exact solutions of nonlinear partial differential equations. It can be applied to nonintegrable equations as well as to integrable ones.
The Principle Of Linearized Stability For Size-Structured Population Models, M. El-Doma
The Principle Of Linearized Stability For Size-Structured Population Models, M. El-Doma
Applications and Applied Mathematics: An International Journal (AAM)
The principle of linearized stability for size-structured population dynamics models is proved giving validity to previous stability results reported in, for example, El-Doma (2008-1). In particular, we show that if all the roots of the characteristic equation lie to the left of the imaginary axis then the steady state is locally exponentially stable, and on the other hand, if there is at least one root that lies to the right of the imaginary axis then the steady state is unstable. We also point out cases when there is resonance
Homotopy Perturbation Method For Solving System Of Generalized Abel’S Integral Equations, Sunil Kumar, Om P. Singh, Sandeep Dixit
Homotopy Perturbation Method For Solving System Of Generalized Abel’S Integral Equations, Sunil Kumar, Om P. Singh, Sandeep Dixit
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, a user friendly algorithm based on the homotopy perturbation method (HPM) is proposed to solve a system of generalized Abel’s integral equations. The stability of the solution under the influence of noise in the input data is analyzed. It is observed that the approximate solutions converge to the exact solutions. Illustrative numerical examples are given to demonstrate the efficiency and simplicity of the proposed method in solving such types of systems of Abel’s integral equations.
Solitary, Explosive, Rational And Elliptic Doubly Periodic Solutions For Nonlinear Electron-Acoustic Waves In The Earth’S Magnetotail Region With Cold Electron Fluid And Isothermal Ions, S. A. El-Wakil, E. M. Abulwafa, M. A. Abdou, E. K. El-Shewy, H. M. Abd-El-Hamid
Solitary, Explosive, Rational And Elliptic Doubly Periodic Solutions For Nonlinear Electron-Acoustic Waves In The Earth’S Magnetotail Region With Cold Electron Fluid And Isothermal Ions, S. A. El-Wakil, E. M. Abulwafa, M. A. Abdou, E. K. El-Shewy, H. M. Abd-El-Hamid
Applications and Applied Mathematics: An International Journal (AAM)
A theoretical investigation has been made of electron acoustic wave propagating in unmagnetized collisionless plasma consisting of a cold electron fluid and isothermal ions with two different temperatures obeying Boltzmann type distributions. Based on the pseudo-potential approach, large amplitude potential structures and the existence of Solitary waves are discussed. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation for small but finite amplitude electrostatic waves. An algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the KdV equation, is …
Dust-Acoustic Solitary Waves In Magnetized Dusty Plasma With Dust Opposite Polarity, S. A. El-Wakil, M. T. Attia, E. K. El-Shewy, S. K. Zaghbeer, H. G. Abdelwahed
Dust-Acoustic Solitary Waves In Magnetized Dusty Plasma With Dust Opposite Polarity, S. A. El-Wakil, M. T. Attia, E. K. El-Shewy, S. K. Zaghbeer, H. G. Abdelwahed
Applications and Applied Mathematics: An International Journal (AAM)
The nonlinear propagation of small but finite amplitude dust-acoustic solitary waves (DAWs) in magnetized collision less dusty plasma has been investigated. The fluid model is a four component magnetized dusty plasma, consisting of positive and negative dust species, isothermal electrons and ions in the presence of an external magnetic field. A reductive perturbation method was employed to obtain the Zakharov Kuznetsov (ZK) equation for the first-order potential. The effects of the presence of positively charged dust fluid, the external magnetic field, and the obliqueness are obtained. The results of the present investigation may be applicable to some plasma environments, such …
Analytic Investigation Of The Kp-Joseph-Egri Equation For Traveling Wave Solutions, N. Taghizadeh, M. Mirzazadeh
Analytic Investigation Of The Kp-Joseph-Egri Equation For Traveling Wave Solutions, N. Taghizadeh, M. Mirzazadeh
Applications and Applied Mathematics: An International Journal (AAM)
By means of the two distinct methods, the cosine-function method and the (G /G ) expansion method, we successfully performed an analytic study on the KP-Joseph-Egri (KP-JE) equation. We exhibited its further closed form traveling wave solutions which reduce to solitary and periodic waves.