Generalized Sumudu Transform and Tempered ξ-Caputo Fractional Derivative

Abstract

This paper applied the generalized Sumudu transform to the tempered ξ-Hilfer fractional integral and the tempered ξ-Caputo fractional derivative. Our findings are utilized to address a nonhomogeneous linear fractional differential equation in an initial value problem involving the tempered ξ-Caputo fractional derivative of an order ς for n − 1 < ς < n ∈ N. An example is provided for 0 < ς < 1.