Fractional partial Differential Equations for Laplace transformation Caputo-Fabrizio and Volterra integration
Author:
Dr. Mariam ALmahdi Mohammed Mulla
Abstract: In this paper we note the numerical methods for solving fractional differential equations, defined in the derivative of the Caputo-Fabrizio fractional operator and Laplace transform of fractional derivatives for integer order, solving differential equation problems using the Laplace transform method, and reducing to Volterra's integral equation, Laplace transform of the Mittage–Leffler function, this problem is not easy to solve analytically because an analytical solution is sometimes not available, even if an analytical solution is available, but it is complected, time-consuming and expensive, so we need to develop a numerical method to address the relevant problem, Analyze a precise result such as the integral or exact expression of a solution to obtain a qualitative answer that shows us what is happening with each variable while numerical methods are more adaptable in the approximate result to obtain quantitative results by iteratively creating an approximate solution sequence for mathematical problems. The method will solve a non-homogeneous linear differential equation directly, following basic steps, without having to solve the integral equation and solutions separately and non-linear differential equations with the rational factor by developing analytical or numerical techniques to find approximate solutions. Finally, we studied some applications, especially for nonlinear differential equations with the rational operator. Keywords: Laplacian Transform Interpretation, fractional Caputo–Fabrizio derivative operator, the Volterra Integral Equation, Existence and uniqueness, Iterative Laplace transform method. Download PDF
|
|
Academic Journal of Research and Scientific Publishing
doi.org/10.52132/Ajrsp.e.2023.54.4