A novel numerical method for solving the Caputo-Fabrizio fractional differential equation
Sadia Arshad, Iram Saleem, Ali Akgül, Jianfei Huang, Yifa Tang, Sayed M. Eldin
Abstract
<abstract><p>In this paper, a unique and novel numerical approach—the fractional-order Caputo-Fabrizio derivative in the Caputo sense—is developed for the solution of fractional differential equations with a non-singular kernel. After converting the differential equation into its corresponding fractional integral equation, we used Simpson's $ 1/3 $ rule to estimate the fractional integral equation. A thorough study is then conducted to determine the convergence and stability of the suggested method. We undertake numerical experiments to corroborate our theoretical findings.</p></abstract>
Topics & Concepts
Fractional calculusMathematicsConvergence (economics)Stability (learning theory)Differential equationKernel (algebra)Mathematical analysisOrder (exchange)Applied mathematicsPure mathematicsComputer scienceMachine learningEconomicsFinanceEconomic growthFractional Differential Equations SolutionsIterative Methods for Nonlinear EquationsMathematical functions and polynomials