Solution of linear and non-linear partial differential equation of fractional order

Abstract

We know that the solution of partial differential equations by analytical method is better than the solution by approximate or series solution method. In this paper, we discuss the solution of linear and non-linear fractional partial differential equations involving derivatives with respect to time or space variables by converting them into the partial differential equations of integer order. Also we develop an analytical formulation to solve such fractional partial differential equations. Moreover, we discuss the method to solve the fractional partial differential equations in space as well as time variables simultaneously with the help of some examples

Solving Nonlinear Time-Fractional Partial Differential Equations Using Conformable Fractional Reduced Differential Transform with Adomian Decomposition Method

“…Recently, Keskin et al [26] have introduced the reduced differential transform method (RDTM) for partial differential equations and the FRDTM found in [26][27]. Muneshwar et al [28] have found the solution of linear and nonlinear FPDEs considering partial differential equations of integer order that involve derivatives with regard to time or space variables. In [29], Kumar et al developed a new version of the L1-predictor-corrector (L1-PC) approach for solving multiple delay-type FDEs.…”

Simulation of Fractional Order 2D-Mathematical Model Using α-Fractional Differential Transform Method

“…In [27], we developed the notion of α-fractional derivative and integral by making the conventional changes in the classical definition of a derivative, which is defined as follows:…”