Abstract
This article aims to establish certain image formulas associated with the fractional calculus operators with Appell function in the kernel and Caputo-type fractional differential operators involving Srivastava polynomials and extended Mittag-Leffler function. The main outcomes are presented in terms of the extended Wright function. In addition, along with the noted outcomes, the implications are also highlighted.
Highlights
IntroductionLeffler function is the most significant in the theory of special functions in literature; solutions are available to number of problems formulated in terms of fractional integral, differential, and difference equations
Introduction and preliminaries The MittagLeffler function is the most significant in the theory of special functions in literature; solutions are available to number of problems formulated in terms of fractional integral, differential, and difference equations
2 Fractional calculus of extended Mittag-Leffler function we present certain image formulas for product of Srivastava polynomials and generalized EMLF in view of the generalized fractional integral and differential calculus and consider some corollaries as particular cases
Summary
Leffler function is the most significant in the theory of special functions in literature; solutions are available to number of problems formulated in terms of fractional integral, differential, and difference equations. It has become a subject of interest for many authors in the field of fractional calculus (FC) and its applications (see details [4, 9, 18, 22, 25, 27, 28, 31, 35, 41,42,43]). Other significant applications are available in the area of fractals kinetics [3, 5, 6], medical sciences [11, 17, 21], fractal calculus and applications [1, 8, 24], and in the Haar wavelet and analytical approach [14, 19, 20, 36].
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