Generalized Sumudu transform and tempered ξ-Caputo fractional derivative

Abstract

This paper applied the generalized Sumudu transform to the tempered ?-Hilfer fractional integral and the tempered ?-Caputo fractional derivative. Our findings are utilized to address non homo-geneous linear fractional differential equations in an initial value problem involving the tempered ?-Caputo fractional derivative of an order ? for n-1 < ? < n ? N. An example is provided for 0 < ? < 1.