scholarly journals Fractional calculus of a product of multivariable Srivastava polynomial and multi-index Bessel function in the kernel F3

2020 ◽  
Vol 5 (2) ◽  
pp. 1462-1475 ◽  
Author(s):  
Owais Khan ◽  
◽  
Nabiullah Khan ◽  
Kottakkaran Sooppy Nisar ◽  
Mohd. Saif ◽  
...  
Keyword(s):  
Fractional Calculus ◽  
Bessel Function ◽  
Multi Index

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.

A family of hyper-Bessel functions and convergent series in them

2014 ◽  
Vol 17 (4) ◽  
Author(s):  
Jordanka Paneva-Konovska
Keyword(s):  
Power Series ◽  
Bessel Function ◽  
Classical Theory ◽  
Bessel Functions ◽  
Differential Operators ◽  
Arbitrary Order ◽  
Convergent Series ◽  
Multi Index ◽  
Fatou Theorem ◽  
Convergence Of Series

AbstractThe Delerue hyper-Bessel functions that appeared as a multi-index generalizations of the Bessel function of the first type, are closely related to the hyper-Bessel differential operators of arbitrary order, introduced by Dimovski. In this work we consider an enumerable family of hyper-Bessel functions and study the convergence of series in such a kind of functions. The obtained results are analogues to the ones in the classical theory of the widely used power series, like Cauchy-Hadamard, Abel and Fatou theorem.

scholarly journals Integral transforms of an extended generalized multi-index Bessel function

2020 ◽  
Vol 5 (6) ◽  
pp. 7531-7546 ◽  
Author(s):  
Shahid Mubeen ◽  
◽  
Rana Safdar Ali ◽  
Iqra Nayab ◽  
Gauhar Rahman ◽  
...  
Keyword(s):  
Bessel Function ◽  
Integral Transforms ◽  
Multi Index

scholarly journals Generalized fractional calculus of the multiindex Bessel function

2017 ◽  
Vol 01 (01) ◽  
pp. 26-32 ◽  
Author(s):  
D. L. Suthar ◽  
S. D. Purohit ◽  
R. K. Parmar
Keyword(s):  
Fractional Calculus ◽  
Bessel Function ◽  
Generalized Fractional Calculus

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.

Differential and integral relations in the class of multi-index Mittag-Leffler functions

2018 ◽  
Vol 21 (1) ◽  
pp. 254-265 ◽  
Author(s):  
Jordanka Paneva-Konovska
Keyword(s):  
Fractional Calculus ◽  
Fractional Order ◽  
Fractional Integration ◽  
Multi Index ◽  
Generalized Fractional Calculus ◽  
Special Cases ◽  
Integral Relations ◽  
Derivatives Of ◽  
Prabhakar Function

Abstract As recently observed by Bazhlekova and Dimovski [1], the n-th derivative of the 2-parametric Mittag-Leffler function gives a 3-parametric Mittag-Leffler function, known as the Prabhakar function. Following this analogy, the n-th derivative of the (2m-index) multi-index Mittag-Leffler functions [6] is obtained, and it turns out that it is expressed in terms of the (3m-index) Mittag-Leffler functions [10, 11]. Further, some special cases of the fractional order Riemann-Liouville and Erdélyi-Kober integrals of the Mittag-Leffler functions are calculated and interesting relations are proved. Analogous relations happen to connect the 3m-Mittag-Leffler functions with the integrals and derivatives of 2m-Mittag-Leffler functions. Finally, multiple Erdélyi-Kober fractional integration operators, as operators of the generalized fractional calculus [5], are shown to relate the 2m- and 3m-parametric Mittag-Leffler functions.

scholarly journals The Marichev-Saigo-Maeda Fractional Calculus Operators Pertaining to the V -Function

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
S. Chandak ◽  
Biniyam Shimelis ◽  
Nigussie Abeye ◽  
A. Padma
Keyword(s):  
Fractional Calculus ◽  
Bessel Function ◽  
Hypergeometric Function ◽  
Exponential Function ◽  
Special Functions ◽  
Generalized Hypergeometric Function ◽  
Generalized Bessel Function ◽  
Fractional Calculus Operators

In the present paper, we establish some composition formulas for Marichev-Saigo-Maeda (MSM) fractional calculus operators with V -function as the kernel. In addition, on account of V -function, a variety of known results associated with special functions such as the Mittag-Leffler function, exponential function, Struve’s function, Lommel’s function, the Bessel function, Wright’s generalized Bessel function, and the generalized hypergeometric function have been discovered by defining suitable values for the parameters.

scholarly journals Estimation of certain integrals with extended multi-index Bessel function

2019 ◽  
Vol 7 (2) ◽  
pp. 206-212 ◽  
Author(s):  
M. Kamarujjama ◽  
N.U. Khan ◽  
Owais Khan
Keyword(s):  
Bessel Function ◽  
Multi Index
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