Solution of systems of linear Caputo fractional Volterra integro-differential equations using the Khalouta integral transform method

The Khalouta integral transform is a powerful method for solving various types of equations, including integro-differential equations and integral equations. It can also be applied to initial and boundary value problems associated with ordinary differential equations and partial differential equations with constant coefficients. The main objective of this paper is to derive solutions to systems of linear Caputo fractional Volterra integro-differential equations using the Khalouta integral transform. To solve such systems using this technique, it is essential to establish and define several key properties of the Khalouta integral transform, which are crucial for deriving the transformation of the Caputo fractional derivative appearing in the systems. Several numerical examples are presented and solved by using the Khalouta integral transform method to demonstrate the applicability of the proposed approach. The results obtained from these numerical examples confirm that the proposed method is highly efficient and provides exact solutions for systems of linear fractional Volterra integro-differential equations in a straightforward manner.