On the Approximation of Fractal-Fractional Differential Equations Using Numerical Inverse Laplace Transform Methods

Laplace transform is one of the powerful tools for solving differential equations in engineering and other science subjects. Using equations, however, sometimes leads to solutions domain that are not readily invertible real by analytical means. Thus, we need numerical inversion methods convert obtained solution from a domain. In this paper, propose scheme based on inverse approximate fractal-fractional with order . Our proposed three main steps. First, given equation fractional-differential Riemann-Liouville sense, then into Caputo sense. Secondly, fractional sense an equivalent space. Then transformed Finally, converted using transform. Three evaluated their convergence also discussed. test problems used validate methods. We demonstrate our results help tables figures. The show Euler’s Talbot’s performed better than Stehfest’s method.