Approximate Solution to Fractional Order Models Using a New Fractional Analytical Scheme

Abstract

In the present work, a new fractional analytical scheme (NFAS) is developed to obtain the approximate results of fourth-order parabolic fractional partial differential equations (FPDEs). The fractional derivatives are considered in the Caputo sense. In this scheme, we show that a Taylor series destructs the recurrence relation and minimizes the heavy computational work. This approach presents the results in the sense of convergent series. In addition, we provide the convergence theorem that shows the authenticity of this scheme. The proposed strategy is very simple and straightforward for obtaining the series solution of the fractional models. We take some differential problems of fractional orders to present the robustness and effectiveness of this developed scheme. The significance of NFAS is also shown by graphical and tabular expressions.

Application of the Double Sumudu-Generalized Laplace Transform Decomposition Method to Solve Singular Pseudo-Hyperbolic Equations

“…The approximate solution of multidimensional diffusion problems under an ABC fractional order derivative has been discussed by Nadeem et al in [10]. The authors of [11] developed a new method which is called a fractional analytical scheme in order to obtain the approximate results of fourth-order parabolic fractional partial differential equations. The authors of [12] have examined the solution of singular linear and nonlinear one-dimensional pseudo-hyperbolic equations through the double Laplace decomposition method.…”