A novel series method for fractional diffusion equation within Caputo fractional derivative

Abstract

In this paper, we suggest the series expansion method for finding the series solution for the time-fractional diffusion equation involving Caputo fractional derivative.

A New Variational Iteration Method for a Class of Fractional Convection-Diffusion Equations in Large Domains

“…This approach can be performed in a trustworthy and effective way and also can handle the fractional differential Equation (7). When the VIM with an auxiliary parameter is applied to solve the fractionel convection-diffusion equations, the linear operator L is defined as L = ∂ α ∂t α , and the Lagrange multiplier λ is identified optimally via variational theory as:…”

“…Theorem 3. [57,58] Suppose that the series solution u(x, t) = v 0 (x, t) + ∑ ∞ n=1 v n (x, t,h), defined in (15), is convergent to exact solution of the nonlinear problem (7). If the truncated series u N (x, t) = v 0 (x, t) + ∑ N n=1 v n (x, t,h), is used as an approximate solution, then the maximum error is estimated as:…”

“…Fractional differential equations (FDEs) have attracted the attention of many researchers owing to their varied applications in science and engineering such as acoustics, control, viscoelasticity, edge detection, and signal processing [3][4][5]. Recently, fractional diffusion equations have been considered using the Adomian decomposition method and series expansion method by authors of [6,7]. Fractional Maxwell fluid within a fractional Caputo-Fabrizio derivative operator using an analytical method was considered in [8].…”

A Note on Conformable Double Laplace Transform and Singular Conformable Pseudoparabolic Equations

“…e parabolic equation appeared in different fields of applied mathematics, such as heat conduction and fluid mechanics (for instance, see [1][2][3][4]). e authors in [5,6] studied the fractional diffusion equations problems by using the Adomian decomposition method and series expansion method. Many papers exist in the literature, which are related to conformable fractional derivative with its properties and applications [7,8].…”

Approximate analytic solutions of multi-dimensional fractional heat-like models with variable coefficients

“…6B, pp. 3725-3729 [7] and was used to solve the fractional 1-D heat-like equations with variable coefficients [8]. The target of the paper is to solve the 2-D and 3-D fractional heat-like models with variable coefficients.…”