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In this paper, our aim is to finding the solutions of the fractional kinetic equation related with the p , q -Mathieu-type series through the procedure of Sumudu and Laplace transforms. The outcomes of fractional kinetic equations in terms of the Mittag-Leffler function are presented. [ABSTRACT FROM AUTHOR]

In this paper, we aim to determine some results of the generalized Bessel–Maitland function in the field of fractional calculus. Here, some relations of the generalized Bessel–Maitland functions and the Mittag-Leffler functions are considered. We develop Saigo and Riemann–Liouville fractional integral operators by using the generalized Bessel–Maitland function, and results can be seen in the form of Fox–Wright functions. We establish a new operator Z ν , η , ρ , γ , w , a + μ , ξ , m , σ ϕ and its inverse operator D ν , η , ρ , γ , w , a + μ , ξ , m , σ ϕ , involving the generalized Bessel–Maitland function as its kernel, and also discuss its convergence and boundedness. Moreover, the Riemann–Liouville operator and the integral transform (Laplace) of the new operator have been developed. [ABSTRACT FROM AUTHOR]

The fundamental aim of this paper is to construct (h, q)-Genocchi numbers and polynomials with weight α.We shall obtain some interesting relations by using p-adic q-integral on ℤp; in the sense of fermionic. Also, we shall derive the (h, q)-extensions of zeta type functions with weight α from the (h, q) a Mellin transformation of this generating function which interpolates the (h, q)-Genocchi numbers and polynomials with weight α at negative integers. [ABSTRACT FROM AUTHOR]