On Weighted (<i>k</i>, <i>s</i>)-Riemann-Liouville Fractional Operators and Solution of Fractional Kinetic Equation

Abstract

In this article, we establish the weighted (k,s)-Riemann-Liouville fractional integral and differential operators. Some certain properties of the operators and the weighted generalized Laplace transform of the new operators are part of the paper. The article consists of Chebyshev-type inequalities involving a weighted fractional integral. We propose an integro-differential kinetic equation using the novel fractional operators and find its solution by applying weighted generalized Laplace transforms.

Keywords

• weighted (<i>k,s</i>) fractional integral operator
• weighted (<i>k,s</i>) fractional derivative
• weighted generalized Laplace transform
• fractional kinetic equation