Numerical Approach for Finding the Solution of Single Term Nonlinear Fractional Differential Equation

Abstract

Here in this paper nonlinear fractional differential equation and its solution have been presented. Fractional Calculus is nothing but the generalization of integer order calculus and due to its complexity, it has not explored much but nature understands the language of fractional calculus more than classical calculus which helps it to find its application in every field of science and technology. It is not easy to approximate the fractional differential equation (FDE) easily but few efficient methods are used efficiently to approximate linear as well as nonlinear FDE. Such a numerical approach is Adam's Predictor-Corrector method that are extensively used to approximate linear as well as nonlinear FDE. Here Adam's Predictor-Corrector method is used to approximate single term nonlinear FDE with an example which shows different results for separate use of Predictor, Corrector as well as both Predictor and Corrector to approximate nonlinear FDE which also shows the numerical efficiency of each terms to approximate nonlinear FDE that will help in improvement of the result of numerical approximation. All simulations have been done in MATLAB. © 2020 IEEE.