Two efficient methods for solving fractional Lane–Emden equations with conformable fractional derivative

Abstract

In this paper, we introduce two reliable efficient approximate methods for solving a class of fractional Lane-Emden equations with conformable fractional derivative (CL-M) which are the so-called conformable Homotopy-Adomian decomposition method (CH-A) and conformable residual power series method (CRP). Furthermore, the proposed methods express the solutions of the non-linear cases of the CL-M in terms of fractional convergent series in which its components can be computed in an easy manner. Finally, the results are given by graphs for each case of the CL-M at different values of α in order to demonstrate its accuracy, applicability, and efficiency.

Solving fractional time-delay diffusion equation with variable-order derivative based on shifted Legendre–Laguerre operational matrices

“…In recent decades, fractional calculus (FC) has played a significant role in science and engineering, and therefore, the scientists focused on its applications to model the real phenomena [2,23,24,29]. The fractional derivative and integrals were recognized to be an efficient tool to describe the properties of complex dynamical processes more accurately than the standard integer derivative and integral [14,17,21,27,38]. Fractional partial differential equations (FPDEs) are a fascinating subject, because they are frequently used to explain a variety of phenomena in real-world situations, including signal processing control theory, fluid flow, potential theory, information theory, finance, and entropy [7,9,25,32].…”

Semi-Analytic Technique for Solving Fractional Partial Differential Equations with Conformable Derivatives

“…Ҫenesiz et al [13] gets new exact solutions of the conformable Burger's type equations. The reader can also see the references [14,15,16], which have been also focus on the numerical and approximate solutions of (CFDEs).…”