Solutions for Hilfer-Type Linear Fractional Integro-Differential Equations with a Variable Coefficient

Abstract

In this paper, we derive an explicit formula of solutions to Hilfer linear fractional integro-differential equations with a variable coefficient in a weighted space, and obtain the existence and uniqueness of solutions for fractional kinetic equations and fractional integro-differential equations with a generalized Mittag–Leffler function. An example is given to illustrate the result obtained.

Keywords

• Hilfer fractional differential equation
• variable coefficient
• generalized Mittag–Leffler function
• weighted space