Perturbed Akbari-Ganji Method for the Solution of Singular Multi-Order Fractional Differential Equations

Abstract

Differential equations, which involve derivatives, are fundamental in describing various physical and engineering phenomena. Newton’s second law of motion provides a basic example, which illustrates how force, mass, and acceleration relate through differential equations. These equations are widely used in science and engineering to model real-world systems. Fractional differential equations extend this concept by incorporating non-integer derivatives, allowing for a more generalized approach to complex problems. Multi-order fractional equations involve multiple fractional derivatives, while singular fractional equations contain terms that become undefined at specific points. We aim to explore the significance of fractional and singular fractional differential equations in mathematical modeling, highlighting their applications in capturing intricate behaviors across different fields and our results emphasize the broader applicability of these equations in solving advanced problems in physics, engineering, and applied sciences.