On certain fractional calculus operators and applications in mathematical physics

Abstract

In this paper, we modify the (k, s) fractional integral operator involving k-Mittag-Leffler function and discuss its properties. We originate a new fractional operator named (k, s)-Prabhakar derivative and obtained some classical fractional operators as a special case of the newly proposed derivative. Some properties of the introduced operator are also part of the present work. The generalized Laplace transform is employed to study the characteristics of fractional operators. We modeled the free-electron laser (FEL) equation by involving the proposed derivative and can find the solution by using the said Laplace transform.

Certain Integral and Differential Formulas Involving the Product of Srivastava’s Polynomials and Extended Wright Function

“…Unified integral representations of some of its special cases are also derived. The extended Wright function is related to Mittag-Leffler function (9), Meijer G-function (10) and Fox H-function (11), therefore all obtained results can be expressed in the form of these functions as well. Moreover, the general class of polynomials gives many known classical orthogonal polynomials as special cases for given suitable values for the coefficient G c,k .…”

“…A new class of integrals associated with hypergeometric function is established by Rakha et al [9]. Certain fractional calculus operators and their applications are briefly discussed by Samraiz et al [10]. A brief discussion of generalized Mittag-Leffler function and multivariable Mittag-Leffler function via generalized fractional calculus operators is available in [11,12].…”

New fractional integral formulas and kinetic model associated with the hypergeometric superhyperbolic sine function

“…Fractional calculus plays an essential role in depicting the complex nonlinear phenomena, [1][2][3][4] for example, mathematical physics, 5 fluid mechanics, 6 viscoelastic mechanics, 7 condensed matter physics, 8 and neural network. 9 Fractional differential equations appear more and more frequently for modeling of relevant systems in several fields of applied sciences.…”

Hermite-Hadamard Fractional Integral Inequalities via Abel-Gontscharoff Green’s Function

“…This theory has gained significant prominence in recent decades due to its wide applications in mathematical sciences. Samraiz et al [1,2] explored some new fractional operators and their applications in mathematical physics. Tarasov [3] and Mainardi [4] explained, in detail, the history and applications of fractional calculus in mathematical economics and finance.…”