Generalized Fractional Integral Operators Pertaining to the Product of Srivastava’s Polynomials and Generalized Mathieu Series

Abstract

Fractional calculus image formulas involving various special functions are important for evaluation of generalized integrals and to obtain the solution of differential and integral equations. In this paper, the Saigo’s fractional integral operators involving hypergeometric function in the kernel are applied to the product of Srivastava’s polynomials and the generalized Mathieu series, containing the factor x λ ( x k + c k ) − ρ in its argument. The results are expressed in terms of the generalized hypergeometric function and Hadamard product of the generalized Mathieu series. Corresponding special cases related to the Riemann–Liouville and Erdélyi–Kober fractional integral operators are also considered.

Solution of Fractional Kinetic Equations Associated with the p,q-Mathieu-Type Series

“…Inspired fundamentally by the works of Cerone and Lenard [14] (see also [16]), Srivastava and Tomovski established a generalized Mathieu series family in [17].…”

Fractional operators with generalized Mittag-Leffler k-function

“…In the literature of fractional calculus, it is distinctly observed that the fractional integral operators and fractional integral formulas containing special functions occupied an influential place in computational and applied mathematics [19][20][21]. The fractional calculus of various types of special functions is used in many research papers [22][23][24][25]. For more details about the recent works in the field of dynamic system theory, stochastic systems, nonequilibrium statistical mechanics, and quantum mechanics, we refer the interesting readers to [26][27][28][29][30][31][32].…”