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- Adomian decomposition method (2)
- Fractional integral operators (2)
- Gamma function (2)
- Generalized hypergeometric functions (2)
- Hypergeometric functions (2)
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- 2-dimensional Pexider quadratic functional equation (1)
- Aleph function (1)
- Analytical scheme (1)
- Appell function F3 (1)
- Approximate solution (1)
- Bessel function (1)
- Beta Functions (1)
- Burgess equation (1)
- Caputo derivative (1)
- Caputo’s fractional derivative (1)
- Chebyshev polynomials (1)
- Chebyshev type inequalities (1)
- Classical Jacobi polynomials (1)
- Convergent series (1)
- Decomposition formula (1)
- Definite integrals (1)
- Extended Mittag-Leffler functions (1)
- Extended Riemann Liouville Fractional derivative operator (1)
- FTE ST (1)
- Fox’s H-function (1)
- Fractional Brownian motion (1)
- Fractional calculus (1)
- Fractional derivative (1)
- Fractional differential equations (1)
- Fractional integral operators by Saigo (1)
Articles 1 - 15 of 15
Full-Text Articles in Analysis
(R1885) Analytical And Numerical Solutions Of A Fractional-Order Mathematical Model Of Tumor Growth For Variable Killing Rate, N. Singha, C. Nahak
(R1885) Analytical And Numerical Solutions Of A Fractional-Order Mathematical Model Of Tumor Growth For Variable Killing Rate, N. Singha, C. Nahak
Applications and Applied Mathematics: An International Journal (AAM)
This work intends to analyze the dynamics of the most aggressive form of brain tumor, glioblastomas, by following a fractional calculus approach. In describing memory preserving models, the non-local fractional derivatives not only deliver enhanced results but also acknowledge new avenues to be further explored. We suggest a mathematical model of fractional-order Burgess equation for new research perspectives of gliomas, which shall be interesting for biomedical and mathematical researchers. We replace the classical derivative with a non-integer derivative and attempt to retrieve the classical solution as a particular case. The prime motive is to acquire both analytical and numerical solutions …
(R1454) On Reducing The Linearization Coefficients Of Some Classes Of Jacobi Polynomials, Waleed Abd-Elhameed, Afnan Ali
(R1454) On Reducing The Linearization Coefficients Of Some Classes Of Jacobi Polynomials, Waleed Abd-Elhameed, Afnan Ali
Applications and Applied Mathematics: An International Journal (AAM)
This article is concerned with establishing some new linearization formulas of the modified Jacobi polynomials of certain parameters. We prove that the linearization coefficients involve hypergeometric functions of the type 4F3(1). Moreover, we show that the linearization coefficients can be reduced in several cases by either utilizing certain standard formulas, and in particular Pfaff-Saalschütz identity and Watson’s theorem, or via employing the symbolic algebraic algorithms of Zeilberger, Petkovsek, and van Hoeij. New formulas for some definite integrals are obtained with the aid of the developed linearization formulas.
Approximate 2-Dimensional Pexider Quadratic Functional Equations In Fuzzy Normed Spaces And Topological Vector Space, Mohammad A. Abolfathi, Ali Ebadian
Approximate 2-Dimensional Pexider Quadratic Functional Equations In Fuzzy Normed Spaces And Topological Vector Space, Mohammad A. Abolfathi, Ali Ebadian
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we prove the Hyers-Ulam stability of the 2-dimensional Pexider quadratic functional equation in fuzzy normed spaces. Moreover, we prove the Hyers-Ulam stability of this functional equation, where f, g are functions defined on an abelian group with values in a topological vector space.
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.
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.
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.
Certain Integrals Associated With The Generalized Bessel-Maitland Function, D. L. Suthar, Hafte Amsalu
Certain Integrals Associated With The Generalized Bessel-Maitland Function, D. L. Suthar, Hafte Amsalu
Applications and Applied Mathematics: An International Journal (AAM)
The aim of this paper is to establish two general finite integral formulas involving the generalized Bessel-Maitland functions Jμ,γν,q (z). The result given in terms of generalized (Wright’s) hypergeometric functions pΨq and generalized hypergeometric functions pFq . These results are obtained with the help of finite integral due to Lavoie and Trottier. Some interesting special cases involving Bessel-Maitland function, Struve’s functions, Bessel functions, generalized Bessel functions, Wright function, generalized Mittag-Leffler functions are deduced.
On Extension Of Mittag-Leffler Function, Ekta Mittal, Rupakshi M. Pandey, Sunil Joshi
On Extension Of Mittag-Leffler Function, Ekta Mittal, Rupakshi M. Pandey, Sunil Joshi
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we study the extended Mittag -Leffler function by using generalized beta function and obtain various differential properties, integral representations. Further, we discuss Mellin transform of these functions in terms of generalized Wright hyper geometric function and evaluate Laplace transform, and Whittaker transform in terms of extended beta function. Finally, several interesting special cases of extended Mittag -Leffler functions have also be given.
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.
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.
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.
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 …
On Some Fractional Integral Operators Involving Generalized Gauss Hypergeometric Functions, N. Virchenko, O. Lisetska, S. L. Kalla
On Some Fractional Integral Operators Involving Generalized Gauss Hypergeometric Functions, N. Virchenko, O. Lisetska, S. L. Kalla
Applications and Applied Mathematics: An International Journal (AAM)
The object of this paper is to give a generalization of Gauss hypergeometric function, and to investigate its basic properties. Further, we define some fractional integral operators and their inverses in terms of the Mellin transform. Several well known integral operators, including Saigo operators can be derived from the results established here.
Approximate Analytical Solutions For Fractional Space- And Time- Partial Differential Equations Using Homotopy Analysis Method, Subir, Das, R. Kumar, P. K. Gupta, Hossein Jafari
Approximate Analytical Solutions For Fractional Space- And Time- Partial Differential Equations Using Homotopy Analysis Method, Subir, Das, R. Kumar, P. K. Gupta, Hossein Jafari
Applications and Applied Mathematics: An International Journal (AAM)
This article presents the approximate analytical solutions of first order linear partial differential equations (PDEs) with fractional time- and space- derivatives. With the aid of initial values, the explicit solutions of the equations are solved making use of reliable algorithm like homotopy analysis method (HAM). The speed of convergence of the method is based on a rapidly convergent series with easily computable components. The fractional derivatives are described in Caputo sense. Numerical results show that the HAM is easy to implement and accurate when applied to space- time- fractional PDEs.
Certain Expansion Formulae Involving A Basic Analogue Of Fox’S H-Function, S. D. Purohit, R. K. Yadav, S. L. Kalla
Certain Expansion Formulae Involving A Basic Analogue Of Fox’S H-Function, S. D. Purohit, R. K. Yadav, S. L. Kalla
Applications and Applied Mathematics: An International Journal (AAM)
Certain expansion formulae for a basic analogue of the Fox’s H-function have been derived by the applications of the q-Leibniz rule for the Weyl type q-derivatives of a product of two functions. Expansion formulae involving a basic analogue of Meijer’s G-function and MacRobert’s E-function have been derived as special cases of the main results.