Fractional Calculus of Wright Function with Raizada Polynomial

2018 ◽  
Vol 4 (3) ◽  
pp. 229-246
Author(s):  
Dharmendra Kumar Singh ◽  
Priyanka Umaro
Keyword(s):  
Fractional Calculus ◽  
Wright Function

scholarly journals Some Applications of the Wright Function in Continuum Physics: A Survey

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 198
Author(s):  
Yuriy Povstenko
Keyword(s):  
Heat Conduction ◽  
Fractional Calculus ◽  
Exponential Function ◽  
Nonlocal Elasticity ◽  
Bessel Functions ◽  
Wright Function ◽  
Mainardi Function ◽  
Integral Relations

The Wright function is a generalization of the exponential function and the Bessel functions. Integral relations between the Mittag–Leffler functions and the Wright function are presented. The applications of the Wright function and the Mainardi function to description of diffusion, heat conduction, thermal and diffusive stresses, and nonlocal elasticity in the framework of fractional calculus are discussed.

scholarly journals Some Fractional Calculus Results Pertaining To Mittag-Leffler Type Functions

2017 ◽  
Vol 13 (1) ◽  
pp. 31-48
Author(s):  
Anupama Choudhary ◽  
Devendra Kumar ◽  
Jagdev Singh
Keyword(s):  
Fractional Calculus ◽  
Wright Function ◽  
Fractional Operators ◽  
Multi Index ◽  
Generalized Wright Function ◽  
Engineering And Technology

Abstract In this paper, we study the generalized fractional operators pertaining to the generalized Mittag-Leffler function and multi-index Mittag-Leffler function. Some applications of the established results associated with generalized Wright function are also deduced as corollaries. The results are useful in solving the problems of science, engineering and technology where the Mittag-Leffler function occurs naturally.

scholarly journals Fractional calculus of generalized Lommel-Wright function and its extended Beta transform

2021 ◽  
Vol 6 (8) ◽  
pp. 8276-8293
Author(s):  
Saima Naheed ◽  
◽  
Shahid Mubeen ◽  
Thabet Abdeljawad ◽  
◽  
...  
Keyword(s):  
Fractional Calculus ◽  
Wright Function

scholarly journals Katugampola Fractional Calculus With Generalized k−Wright Function

2021 ◽  
Vol 1 (1) ◽  
pp. 34-44
Author(s):  
Ahmad Y. A. Salamooni ◽  
D. D. Pawar
Keyword(s):  
Fractional Calculus ◽  
Fractional Integrals ◽  
Wright Function ◽  
Fractional Integrals And Derivatives ◽  
Derivatives Of

In this article, we present some properties of the Katugampola fractional integrals and derivatives. Also, we study the fractional calculus properties involving Katugampola Fractional integrals and derivatives of generalized k−Wright function nΦkm(z).

scholarly journals The Marichev-Saigo-Maeda Fractional Calculus Operators Pertaining to the Generalized K-Struve Function

2020 ◽  
Vol 5 (2) ◽  
pp. 593-602
Author(s):  
Seema Kabra ◽  
Harish Nagar ◽  
Kottakkaran Sooppy Nisar ◽  
D.L. Suthar
Keyword(s):  
Fractional Calculus ◽  
Wright Function ◽  
Fractional Calculus Operators

AbstractIn the present paper, we establish some compositions formulas for Marichev-Saigo-Maeda (MSM) fractional calculus operators with k-Struve function S_{\nu ,c}^k as of the kernel. The results are presented in terms of generalized k-Wright function _p\Psi _q^k .

scholarly journals The Marichev-Saigo-Maeda Fractional-Calculus Operators Involving the (p,q)-Extended Bessel and Bessel-Wright Functions

2021 ◽  
Vol 5 (4) ◽  
pp. 210
Author(s):  
Hari M. Srivastava ◽  
Eman S. A. AbuJarad ◽  
Fahd Jarad ◽  
Gautam Srivastava ◽  
Mohammed H. A. AbuJarad
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivative ◽  
Bessel Function ◽  
Fractional Integral ◽  
Hadamard Product ◽  
Gauss Hypergeometric Function ◽  
Wright Function ◽  
Special Cases ◽  
Fractional Calculus Operators ◽  
Fractional Derivative Operators

The goal of this article is to establish several new formulas and new results related to the Marichev-Saigo-Maeda fractional integral and fractional derivative operators which are applied on the (p,q)-extended Bessel function. The results are expressed as the Hadamard product of the (p,q)-extended Gauss hypergeometric function Fp,q and the Fox-Wright function rΨs(z). Some special cases of our main results are considered. Furthermore, the (p,q)-extended Bessel-Wright function is introduced. Finally, a variety of formulas for the Marichev-Saigo-Maeda fractional integral and derivative operators involving the (p,q)-extended Bessel-Wright function is established.

scholarly journals Composition Formulae for the k-Fractional Calculus Operators Associated with k-Wright Function

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
D. L. Suthar
Keyword(s):  
Fractional Calculus ◽  
Hypergeometric Function ◽  
Fractional Order ◽  
Wright Function ◽  
Special Cases ◽  
Fractional Calculus Operators ◽  
Fractional Order Integral

In this article, the k-fractional-order integral and derivative operators including the k-hypergeometric function in the kernel are used for the k-Wright function; the results are presented for the k-Wright function. Also, some of special cases related to fractional calculus operators and k-Wright function are considered.

scholarly journals The Four-Parameters Wright Function of the Second kind and its Applications in FC

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 970 ◽  
Author(s):  
Yuri Luchko
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivatives ◽  
Dimensional Space ◽  
Wide Spectrum ◽  
Operational Calculus ◽  
Fractional Diffusion ◽  
Wright Function ◽  
Scale Invariant ◽  
First Case

In this survey paper, we present both some basic properties of the four-parameters Wright function and its applications in Fractional Calculus. For applications in Fractional Calculus, the four-parameters Wright function of the second kind is especially important. In the paper, three case studies illustrating a wide spectrum of its applications are presented. The first case study deals with the scale-invariant solutions to a one-dimensional time-fractional diffusion-wave equation that can be represented in terms of the Wright function of the second kind and the four-parameters Wright function of the second kind. In the second case study, we consider a subordination formula for the solutions to a multi-dimensional space-time-fractional diffusion equation with different orders of the fractional derivatives. The kernel of the subordination integral is a special case of the four-parameters Wright function of the second kind. Finally, in the third case study, we shortly present an application of an operational calculus for a composed Erdélyi-Kober fractional operator for solving some initial-value problems for the fractional differential equations with the left- and right-hand sided Erdélyi-Kober fractional derivatives. In particular, we present an example with an explicit solution in terms of the four-parameters Wright function of the second kind.

scholarly journals Composition Formulae for the k -Fractional Calculus Operator with the S -Function

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Hagos Tadesse ◽  
Haile Habenom ◽  
Anita Alaria ◽  
Biniyam Shimelis
Keyword(s):  
Fractional Calculus ◽  
Hypergeometric Function ◽  
Fractional Order ◽  
Wright Function ◽  
Integral Transformations ◽  
Special Cases ◽  
Fractional Order Integral

In this study, the S-function is applied to Saigo’s k -fractional order integral and derivative operators involving the k -hypergeometric function in the kernel; outcomes are described in terms of the k -Wright function, which is used to represent image formulas of integral transformations such as the beta transform. Several special cases, such as the fractional calculus operator and the S -function, are also listed.

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