Application of Natural Transform Method to Fractional Pantograph Delay Differential Equations

Abstract

In this paper, a new method based on combination of the natural transform method (NTM), Adomian decomposition method (ADM), and coefficient perturbation method (CPM) which is called “perturbed decomposition natural transform method” (PDNTM) is implemented for solving fractional pantograph delay differential equations with nonconstant coefficients. The fractional derivative is regarded in Caputo sense. Numerical evaluations are included to demonstrate the validity and applicability of this technique.

Study of Convergence of Reduced Differential Transform Method for Different Classes of Differential Equations

“…erefore, the RDTM can overcome the foregoing limitations and restrictions of perturbation techniques and complicated computational so that it provides us with a possibility to analyse accurately nonlinear equations. e RDTM was successfully applied to ordinary differential equations [15], partial differential equations [16][17][18], fractional differential equations [19][20][21][22][23], Volterra integral equation [24][25][26], and integro-differential equations [27][28][29].…”

Machine Learning for Modeling the Singular Multi-Pantograph Equations

“…In Reference [ 14 ], by the use of residual power series, an analytical solution is obtained and the efficiency of using residual power series is compared with Chebyshev and Boubaker polynomials. In Reference [ 15 ], Adomian decomposition approach is used to construct a solution algorithm for MDEs with fractional-order in the sense of Caputo definition. In Reference [ 16 ], by the use of Riemann Liouville fractional derivative and integral definitions, some operational matrices are constructed and then on basis of Jacobi polynomials, an analytical solution is presented.…”