Fractional calculus operators associated with the h-function, laplace, and fourier transforms

Abstract

In this research, we addressed the use of Riemann-Liouville differential operators to solve homogeneous and non-homogenous linear fractional differential equations. These operators are related to the Laplace transform of fractional integral and the convolution of H-Function. The Laplace transform in fractional calculus is a generalization of the Laplace transform in the classical sense, as evidenced by its simplicity, efficiency, and excellent accuracy. In keeping with the answers found in the literature, fractional Laplace transforms are strong and effective methods for obtaining analytic solutions of homogeneous and non-homogenous linear fractional differential equations.