Numerical Analysis of Time-Fractional Diffusion Equations via a Novel Approach

Abstract

The aim of this paper is a new semianalytical technique called the variational iteration transform method for solving fractional-order diffusion equations. In the variational iteration technique, identifying of the Lagrange multiplier is an essential rule, and variational theory is commonly used for this purpose. The current technique has the edge over other methods as it does not need extra parameters and polynomials. The validity of the proposed method is verified by considering some numerical problems. The solution achieved has shown that the better accuracy of the proposed technique. This paper proposes a simpler method to calculate the multiplier using the Shehu transformation, making a valuable technique to researchers dealing with various linear and nonlinear problems.

Three Approximations of Numerical Solution's by Finite Element Method for Resolving Space-Time Partial Differential Equations Involving Fractional Derivative's Order

“…Some different numerical solution methods are proposed to resolve the space and time fractional partial differential equations [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23].…”

Nonlinear Convective SiO2 and TiO2 Hybrid Nanofluid Flow over an Inclined Stretched Surface

“…Kumar et al [43] calculated the numerical outcomes of CNT nanofluids movement by the numerical scheme in divergent and convergent channels under the effects of thermal radiation. Akgül et al [44][45][46][47][48][49] presented different novel technique for investigating fractional differential equations including the Atangana-Baleanu fractional derivative. The relevant and latest literature can be seen as [50][51][52].…”