A modified homotopy analysis method for solution of fractional wave equations

Abstract

The aim of this article is to introduce a modified analytical approach to obtain quick and accurate solution of wave-like fractional physical models. This modified analytical approach is an innovative adjustment in Laplace transform algorithm and homotopy analysis method for fractional partial differential equations. The proposed technique solves the problems using Adomian's polynomials. The homotopy analysis transform method utilizes a simple and powerful method to adjust and control the convergence region of the infinite series solution using an auxiliary parameter. The numerical solutions obtained by this modified proposed method indicate that the approach is easy to implement, highly accurate, and computationally very attractive. A good agreement between the obtained solutions and some well-known results has been obtained.

Application of the Caputo‐Fabrizio and Atangana‐Baleanu fractional derivatives to mathematical model of cancer chemotherapy effect

“…The Laplace homotopy analysis method (LHAM) is a combination of HAM and Laplace transform. [54][55][56] In this work, we formulate a fractional-order cancer chemotherapy effect model via Caputo-Fabrizio and Atangana-Baleanu fractional-order derivatives in the Liouville-Caputo sense. We consider fractional derivatives with nonsingular kernel because of its ability to describe anomalous spread like that of cancer.…”

An efficient computational approach for generalized Hirota-Satsuma coupled KdV equations arising in shallow water waves

“…In recent years many scientists and mathematicians have made paid attention for combining semi analytical techniques with Laplace transform such as Khuri [18], Khan and Hussain [17], Khan et al [15], Gupta et al [12], Kumar et al [21,22], Wazwaz [40], Thongmoon and Pusjuso [38] and others. On the other hand, HAM is also combined with well defined Laplace transform to investigate nonlinear problems such as nonlinear equation semi infinite domain [16], fractional biological population model [20], Volterra integral equation [19], fractional wave equations [43], etc.…”

An efficient computational approach for linear and nonlinear fractional differential equations

“…The q-HAM is introduced and nurtured by El-Tavil and Huseen [7,8] is a modification of homotopy analysis method (HAM) [19,20]. In recent years HAM has also been employed by using Laplace transform algorithm to study mathematical equations such as nonlinear boundary value problem on semi in finite domain [16], nonlinear fractional BBMBerger equation [18], fractional Lotka Volterra equation [26], systems of fractional differential equations [10], linear fractional wave equations [35], fractional partial differential equations arising in physics [33], etc. The q-HATM gives the series solution in considerably large domain, it provides us with a simple way to adjust and control the convergence region of the series solutions by introducing the auxiliary parameter and n, auxiliary function H(x,t), the initial guess u 0 (x, t).…”