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Articles 31 - 60 of 138
Full-Text Articles in Analysis
An Efficient Algorithm For Numerical Inversion Of System Of Generalized Abel Integral Equations, Sandeep Dixit
An Efficient Algorithm For Numerical Inversion Of System Of Generalized Abel Integral Equations, Sandeep Dixit
Applications and Applied Mathematics: An International Journal (AAM)
In this article a direct method is introduced, which is based on orthonormal Bernstein polynomials, to present an efficient and stable algorithm for numerical inversion of the system of singular integral equations of Abel type. The appropriateness of earlier numerical inversion methods was restricted to the one portion of singular integral equations of Abel type. The proposed method is absolutely accurate, and numerical illustrations are given to show the convergence and utilization of the suggested method and comparisons are made with some other existing numerical solution.
On Double Fuzzy M-Open Mappings And Double Fuzzy M-Closed Mappings, J. Sathiyaraj, A. Vadivel, O. U. Maheshwari
On Double Fuzzy M-Open Mappings And Double Fuzzy M-Closed Mappings, J. Sathiyaraj, A. Vadivel, O. U. Maheshwari
Applications and Applied Mathematics: An International Journal (AAM)
We introduce and investigate some new class of mappings called double fuzzy M-open map and double fuzzy M-closed map in double fuzzy topological spaces. Also, some of their fundamental properties are studied. Moreover, we investigate the relationships between double fuzzy open, double fuzzy θ semiopen, double fuzzy δ preopen, double fuzzy M open and double fuzzy e open and their respective closed mappings.
Variants Of Meir-Keeler Fixed Point Theorem And Applications Of Soft Set-Valued Maps, Akbar Azam, Mohammed Shehu Shagari
Variants Of Meir-Keeler Fixed Point Theorem And Applications Of Soft Set-Valued Maps, Akbar Azam, Mohammed Shehu Shagari
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we prove a Meir-Keeler type common fixed point theorem for two mappings for which the range set of the first one is a family of soft sets, called soft set-valued map and the second is a point-to-point mapping. In addition, it is also shown that under some suitable conditions, a soft set-valued map admits a selection having a unique fixed point. In support of the obtained result, nontrivial examples are provided. The novelty of the presented idea herein is that it extends the Meir-Keeler fixed point theorem and the theory of selections for multivalued mappings from the …
Generalized Growth And Faber Polynomial Approximation Of Entire Functions Of Several Complex Variables In Some Banach Spaces, Devendra Kumar, Manisha Vijayran
Generalized Growth And Faber Polynomial Approximation Of Entire Functions Of Several Complex Variables In Some Banach Spaces, Devendra Kumar, Manisha Vijayran
Applications and Applied Mathematics: An International Journal (AAM)
In this paper the relationship between the generalized order of growth of entire functions of many complex variables m (m >= 2) over Jordan domains and the sequence of Faber polynomial approximations in some Banach spaces has been investigated. Our results improve the various results shown in the literature.
Numerical Simulation For Solving Fractional Riccati And Logistic Differential Equations As A Difference Equation, M. M. Khader, N. H. Sweilam, B. N. Kharrat
Numerical Simulation For Solving Fractional Riccati And Logistic Differential Equations As A Difference Equation, M. M. Khader, N. H. Sweilam, B. N. Kharrat
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we introduce a numerical treatment using the generalized Euler method (GEM) for the fractional (Caputo sense) Riccati and Logistic differential equations. In the proposed method, we invert the given model as a difference equation. We compare our numerical solutions with the exact solution and with those numerical solutions using the fourth-order Runge-Kutta method (RK4). The obtained numerical results of the two proposed problem models show the simplicity and efficiency of the proposed method.
A Comparative Study Of Shehu Variational Iteration Method And Shehu Decomposition Method For Solving Nonlinear Caputo Time-Fractional Wave-Like Equations With Variable Coefficients, Ali Khalouta, Abdelouahab Kadem
A Comparative Study Of Shehu Variational Iteration Method And Shehu Decomposition Method For Solving Nonlinear Caputo Time-Fractional Wave-Like Equations With Variable Coefficients, Ali Khalouta, Abdelouahab Kadem
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, a comparative study between two different methods for solving nonlinear Caputo time-fractional wave-like equations with variable coefficients is conducted. These two methods are called the Shehu variational iteration method (SVIM) and the Shehu decomposition method (SDM). To illustrate the efficiency and accuracy of the proposed methods, three different numerical examples are presented. The results obtained show that the two methods are powerful and efficient methods which both give approximations of higher accuracy and closed form solutions if existing. However, the SVIM has an advantage over SDM that it solves the nonlinear problems without using the Adomian polynomials. …
On Fejér Type Inequalities For Convex Mappings Utilizing Generalized Fractional Integrals, A. Kashuri, R. Liko
On Fejér Type Inequalities For Convex Mappings Utilizing Generalized Fractional Integrals, A. Kashuri, R. Liko
Applications and Applied Mathematics: An International Journal (AAM)
In this work, we first establish Hermite-Hadamard-Fejér type inequalities for convex function involving generalized fractional integrals with respect to another function which are generalization of some important fractional integrals such as the Riemann-Liouville fractional integrals and the Hadamard fractional integrals. Moreover, we obtain some trapezoid type inequalities for these kind of generalized fractional integrals. The results given in this paper provide generalization of several inequalities obtained in earlier studies.
Existence Of Resolvent For Conformable Fractional Volterra Integral Equations, Awais Younus, Khizra Bukhsh, Cemil Tunç
Existence Of Resolvent For Conformable Fractional Volterra Integral Equations, Awais Younus, Khizra Bukhsh, Cemil Tunç
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we consider the conformable fractional Volterra integral equation. We study the existence of a resolvent kernel corresponding to conformable fractional Volterra integral equation. The technique of proof involves Lebesgue dominated convergence theorem. Our results improve and extend the results obtained in literature.
Chebyshev Type Inequalities Involving The Fractional Integral Operator Containing Multi-Index Mittag-Leffler Function In The Kernel, S. D. Purohit, N. Jolly, M. K. Bansal, Jagdev Singh, Devendra Kumar
Chebyshev Type Inequalities Involving The Fractional Integral Operator Containing Multi-Index Mittag-Leffler Function In The Kernel, S. D. Purohit, N. Jolly, M. K. Bansal, Jagdev Singh, Devendra Kumar
Applications and Applied Mathematics: An International Journal (AAM)
Recently, several authors have investigated Chebyshev type inequalities for numerous fractional integral operators. Being motivated by the work done by earlier researchers and their numerous applications in probability, transform theory, numerical quadrature, statistical problems and its significance in fractional boundary value problems. We aim to evaluate Chebyshev type inequalities involving fractional integral operator containing multi-index Mittag-Leffler function in the kernel. Admissible connections of the results mentioned in this article to those associated with previously established familiar fractional integral operators have been pointed out.
Ruscheweyh-Goyal Derivative Of Fractional Order, Its Properties Pertaining To Pre-Starlike Type Functions And Applications, Ritu Agarwal, G. S. Paliwal
Ruscheweyh-Goyal Derivative Of Fractional Order, Its Properties Pertaining To Pre-Starlike Type Functions And Applications, Ritu Agarwal, G. S. Paliwal
Applications and Applied Mathematics: An International Journal (AAM)
The study of the operators possessing convolution form and their properties is considered advantageous in geometric function theory. In 1975 Ruscheweyh defined operator for analytic functions using the technique of convolution. In 2005, Goyal and Goyal generalized the Ruscheweyh operator to fractional order (which we call here Ruscheweyh-Goyal differential operator) using Srivastava-Saigo fractional differential operator involving hypergeometric function. Inspired by these earlier efforts, we discuss the properties of the Ruscheweyh-Goyal derivative of arbitrary order. We define a class of pre-starlike type functions involving the Ruscheweyh-Goyal fractional derivative and obtain the inclusion relation. Further, we prove that Ruscheweyh-Goyal derivative operator preserve …
Class Of Integrals Involving Generalized Hypergeometric Function, D. L. Suthar, Teklay Hailay, Hafte Amsalu, Jagdev Singh
Class Of Integrals Involving Generalized Hypergeometric Function, D. L. Suthar, Teklay Hailay, Hafte Amsalu, Jagdev Singh
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we establish some definite integrals involving generalized hypergeometric function, product of algebraic functions, Jacobi function, Legendre function and general class of polynomials. Certain special cases of the main results are also pointed out.
On A Hybrid Technique To Handle Analytical And Approximate Solutions Of Linear And Nonlinear Fractional Order Partial Differential Equations, Kamal Shah, Hammad Khalil, Ahmet Yildirim
On A Hybrid Technique To Handle Analytical And Approximate Solutions Of Linear And Nonlinear Fractional Order Partial Differential Equations, Kamal Shah, Hammad Khalil, Ahmet Yildirim
Applications and Applied Mathematics: An International Journal (AAM)
This manuscript is devoted to consider Natural transform (NT) coupled with homotopy perturbation method (HPM) for obtaining series solutions to some linear and nonlinear fractional partial differential equations (FPDEs). By means of NT, we obtain the transformed problem which is then solved by using HPM. By means of Stehfest’s numerical algorithm and using the dual relationship of NT and Laplace transform, we calculate inverse NT for approximate solutions. The series solutions we obtain using the proposed method are in close agreement with the exact solutions. We apply the proposed method to some interesting problems to illustrate our main results.
Solutions Of The Generalized Abel’S Integral Equation Using Laguerre Orthogonal Approximation, N. Singha, C. Nahak
Solutions Of The Generalized Abel’S Integral Equation Using Laguerre Orthogonal Approximation, N. Singha, C. Nahak
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, a numerical approximation is drafted for solving the generalized Abel’s integral equation by practicing Laguerre orthogonal polynomials. The proposed approximation is framed for the first and second kinds of the generalized Abel’s integral equation. We have utilized the properties of fractional order operators to interpret Abel’s integral equation as a fractional integral equation. It offers a new approach by employing Laguerre polynomials to approximate the integrand of a fractional integral equation. Given examples demonstrate the simplicity and suitability of the method. The graphical representation of exact and approximate solutions helps in visualizing a solution at discrete points, …
Application Of Reduced Differential Transform Method For Solving Two-Dimensional Volterra Integral Equations Of The Second Kind, Seyyedeh R. Moosavi Noori, Nasir Taghizadeh
Application Of Reduced Differential Transform Method For Solving Two-Dimensional Volterra Integral Equations Of The Second Kind, Seyyedeh R. Moosavi Noori, Nasir Taghizadeh
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we propose new theorems of the reduced differential transform method (RDTM) for solving a class of two-dimensional linear and nonlinear Volterra integral equations (VIEs) of the second kind. The advantage of this method is its simplicity in using. It solves the equations straightforward and directly without using perturbation, Adomian’s polynomial, linearization or any other transformation and gives the solution as convergent power series with simply determinable components. Also, six examples and numerical results are provided so as to validate the reliability and efficiency of the method.
On The Weighted Pseudo Almost Periodic Solutions Of Nicholson’S Blowflies Equation, Ramazan Yazgan, Cemil Tunç
On The Weighted Pseudo Almost Periodic Solutions Of Nicholson’S Blowflies Equation, Ramazan Yazgan, Cemil Tunç
Applications and Applied Mathematics: An International Journal (AAM)
This study is concerned with the existence, uniqueness and global exponential stability of weighted pseudo almost periodic solutions of a generalized Nicholson’s blowflies equation with mixed delays. Using some differential inequalities and a fixed point theorem, sufficient conditions were obtained for the existence, uniqueness of at the least a weighted pseudo almost periodic solutions and global exponential stability of this solution. The results of this study are new and complementary to the previous ones can be found in the literature. At the end of the study an example is given to show the accuracy of our results.
New Notions From (R; S)-Generalized Fuzzy E-Open Sets, A. Vadivel, P. Periyasamy, V. Chandrasekar, G. Saravanakumar
New Notions From (R; S)-Generalized Fuzzy E-Open Sets, A. Vadivel, P. Periyasamy, V. Chandrasekar, G. Saravanakumar
Applications and Applied Mathematics: An International Journal (AAM)
The present article discuss (r; s)-generalized fuzzy e-border, (r; s)-generalized fuzzy e-exterior and (r; s)-generalized fuzzy e-frontier in double fuzzy topologies. Furthermore, some characterizations of generalized double fuzzy e-continuous, generalized double fuzzy e-open, generalized double fuzzy e-closed and generalized double fuzzy e-closure-irresolute functions are studied and investigated. Moreover, the interrelations among the new concepts are discussed with some necessary examples.
On The New Generalized Block Difference Sequence Space, Sezer Erdem, Serkan Demiriz
On The New Generalized Block Difference Sequence Space, Sezer Erdem, Serkan Demiriz
Applications and Applied Mathematics: An International Journal (AAM)
In this current study, the most apparent aspect is to submit a new block sequence space. We investigate its topological properties and inclusion relations. Moreover, we consider the problem of finding the norm of certain matrix operators from l_p into this space and apply our results to Copson and Hilbert matrices.
On General Matrix Application Of Quasi Power Increasing Sequences, Hikmet S. Özarslan, Ahmet Karakaş
On General Matrix Application Of Quasi Power Increasing Sequences, Hikmet S. Özarslan, Ahmet Karakaş
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we give a general theorem dealing with absolute matrix summability by using quasi-power increasing sequences. This theorem includes some results concerning absolute summability methods.
Integral Inequalities Of Hermite-Hadamard Type Via Green Function And Applications, Tuba Tunç, Sümeyye Sönmezoğlu, Mehmet Z. Sarıkaya
Integral Inequalities Of Hermite-Hadamard Type Via Green Function And Applications, Tuba Tunç, Sümeyye Sönmezoğlu, Mehmet Z. Sarıkaya
Applications and Applied Mathematics: An International Journal (AAM)
In this study, we establish some Hermite- Hadamard type inequalities for functions whose second derivatives absolute value are convex. In accordance with this purpose, we obtain an identity using Green's function. Then using this equality we get our main results.
Generalized Bagley-Torvik Equation And Fractional Oscillators, Mark Naber, Lucas Lymburner
Generalized Bagley-Torvik Equation And Fractional Oscillators, Mark Naber, Lucas Lymburner
Applications and Applied Mathematics: An International Journal (AAM)
In this paper the Bagley-Torvik Equation is considered with the order of the damping term allowed to range between one and two. The solution is found to be representable as a convolution of trigonometric and exponential functions with the driving force. The properties of the effective decay rate and the oscillation frequency with respect to the order of the fractional damping are also studied. It is found that the effective decay rate and oscillation frequency have a complex dependency on the order of the derivative of the damping term and exhibit properties one might expect of a thermodynamic Equation of …
Generalized Differential Transform Method For Solving Some Fractional Integro-Differential Equations, S. Shahmorad, A. A. Khajehnasiri
Generalized Differential Transform Method For Solving Some Fractional Integro-Differential Equations, S. Shahmorad, A. A. Khajehnasiri
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we use a generalized form of two-dimensional Differential Transform (2D-DT) to solve a new class of fractional integro-differential equations. We express some useful properties of the new transform as a proposition and prove a convergence theorem. Then we illustrate the method with numerical examples.
Transient Thermal Stresses Due To Axisymmetric Heat Supply In A Semi-Infinite Thick Circular Plate, S. D. Warbhe, K. C. Deshmukh
Transient Thermal Stresses Due To Axisymmetric Heat Supply In A Semi-Infinite Thick Circular Plate, S. D. Warbhe, K. C. Deshmukh
Applications and Applied Mathematics: An International Journal (AAM)
The present paper deals with the determination of thermal stresses in a semi-infinite thick circular plate of a finite length and infinite extent subjected to an axisymmetric heat supply. A thick circular plate is considered having constant initial temperature and arbitrary heat flux is applied on the upper and lower face. The governing heat conduction equation has been solved by using integral transform technique. The results are obtained in terms of Bessel’s function. The thermoelastic behavior has been computed numerically and illustrated graphically for a steel plate.
Generalized Growth And Faber Polynomial Approximation Of Entire Functions Of Several Complex Variables In Some Banach Spaces, Devendra Kumar, Manisha Vijayran
Generalized Growth And Faber Polynomial Approximation Of Entire Functions Of Several Complex Variables In Some Banach Spaces, Devendra Kumar, Manisha Vijayran
Applications and Applied Mathematics: An International Journal (AAM)
In this paper the relationship between the generalized order of growth of entire functions of many complex variables m(m ≥ 2) over Jordan domains and the sequence of Faber polynomial approximations in some Banach spaces has been investigated. Our results improve the various results shown in the literature.
Unified Ball Convergence Of Inexact Methods For Finding Zeros With Multiplicity, Ioannis K. Argyros, Santhosh George
Unified Ball Convergence Of Inexact Methods For Finding Zeros With Multiplicity, Ioannis K. Argyros, Santhosh George
Applications and Applied Mathematics: An International Journal (AAM)
We present an extended ball convergence of inexact methods for approximating a zero of a nonlinear equation with multiplicity m; where m is a natural number. Many popular methods are special cases of the inexact method.
Functional Dimension Of Solution Space Of Differential Operators Of Constant Strength, Morteza Shafii-Mousavi
Functional Dimension Of Solution Space Of Differential Operators Of Constant Strength, Morteza Shafii-Mousavi
Applications and Applied Mathematics: An International Journal (AAM)
A differential operator with constant coefficients is hypoelliptic if and only if its solution space is of finite functional dimension. We extend this property to operators with variable coefficient. We prove that an equally strong differential operator with variable coefficients has the same property. In addition, we extend the Zielezny’s result to operators with variable coefficients; prove that an operator with analytic coefficients on ℝn is elliptic if and only if locally the functional dimension of its solution space is the same as the Euclidean dimension n.
Study Of Specially And Temporally Dependent Adsorption Coefficient In Heterogeneous Porous Medium, Dilip K. Jaiswal, Gulrana _
Study Of Specially And Temporally Dependent Adsorption Coefficient In Heterogeneous Porous Medium, Dilip K. Jaiswal, Gulrana _
Applications and Applied Mathematics: An International Journal (AAM)
One-dimensional advection-dispersion equation (ADE) is studied along unsteady longitudinal flow through a semi-infinite heterogeneous medium. Adsorption coefficient is considered temporally and spatially–dependent function i.e., expressed in degenerate form. The dispersion parameter is considered as inversely proportional to adsorption coefficient. The input source is of pulse type. The Laplace Transformation Technique (LTT) is used to obtain the analytical solution by introducing certain new independent variables through separate transformations. The effects of adsorption, heterogeneity and unsteadiness are investigated and discussed with the help of various graphs.
Some Results Of Double Sequences In 2-Normed And N-Normed Spaces, P. R. Kavyasree, B. Surender Reddy
Some Results Of Double Sequences In 2-Normed And N-Normed Spaces, P. R. Kavyasree, B. Surender Reddy
Applications and Applied Mathematics: An International Journal (AAM)
The primary purpose of this paper is to introduce the notion of double sequences in 2-normed space. We provide a simple way to derive a norm from the standard 2-norm by using double sequences when a 2-normed space is given. Equivalence relation between derived norm and the usual norm are established. Using this derived norm, we examine the completeness property of a 2-normed space and we extend the results to n-normed spaces.
Birkhoff’S Ergodic Theorem For Weighted Variable Exponent Amalgam Spaces, Ismail Aydın, Cihan Unal
Birkhoff’S Ergodic Theorem For Weighted Variable Exponent Amalgam Spaces, Ismail Aydın, Cihan Unal
Applications and Applied Mathematics: An International Journal (AAM)
In this study, we consider some properties of weighted variable exponent Lebesgue and amalgam spaces. It is known these spaces are considerably used in harmonic and time-frequency analysis including elastic mechanics, electrorheological fluids, image processing, etc. Ergodic theory investigates the long-term averaging properties of measure preserving dynamical systems. This theory has also several applications and problems of statistical physics and mechanics. Moreover, it has influence on many areas of mathematics, especially probability theory and dynamical systems as well as Fourier analysis, functional analysis, and group theory. Therefore, we investigate Ergodic theorem for unweighted variable exponent Lebesgue spaces and also an …
Some Midpoint Type Inequalities For Riemann Liouville Fractional Integrals, Zeynep Şanli
Some Midpoint Type Inequalities For Riemann Liouville Fractional Integrals, Zeynep Şanli
Applications and Applied Mathematics: An International Journal (AAM)
In the literature, there are a lot of studies about midpoint type inequalities for Riemann Liouville Fractional Integrals. But for most of them, the right and left fractional integrals are used together. In this paper, we give three new Riemann-Liouville fractional midpoint type identities for differentiable functions by using only the right or the left fractional integral. From these identities, we obtain some new midpoint type inequalities for harmonically convex functions by applying power mean and Hölder inequalities.
Approximate Analytical Solutions Of Space-Fractional Telegraph Equations By Sumudu Adomian Decomposition Method, Hasib Khan, Cemil Tunç, Rahmat A. Khan, Akhtyar G. Shirzoi, Aziz Khan
Approximate Analytical Solutions Of Space-Fractional Telegraph Equations By Sumudu Adomian Decomposition Method, Hasib Khan, Cemil Tunç, Rahmat A. Khan, Akhtyar G. Shirzoi, Aziz Khan
Applications and Applied Mathematics: An International Journal (AAM)
The main goal in this work is to establish a new and efficient analytical scheme for space fractional telegraph equation (FTE) by means of fractional Sumudu decomposition method (SDM). The fractional SDM gives us an approximate convergent series solution. The stability of the analytical scheme is also studied. The approximate solutions obtained by SDM show that the approach is easy to implement and computationally very much attractive. Further, some numerical examples are presented to illustrate the accuracy and stability for linear and nonlinear cases.