Abstract:
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.
Fulltext:
PDF file (1006 kB)
The content is published under the terms of the Creative Commons Attribution 4.0 International License
