Approximate solution for fractional attractor one-dimensional Keller-Segel equations using homotopy perturbation sumudu transform method

Abstract

In this paper, homotopy perturbation sumudu transform method (HPSTM) is proposed to solve fractional attractor one-dimensional Keller-Segel equations. The HPSTM is a combined form of homotopy perturbation method (HPM) and sumudu transform using He’s polynomials. The result shows that the HPSTM is very efficient and simple technique for solving nonlinear partial differential equations. Test examples are considered to illustrate the present scheme.

A Computational Approach for the Calculation of Temperature Distribution in Casting-Mould Heterogeneous System with Fractional Order

“…The homotopy perturbation technique (HPM) [ 11 ] is a well-known method for obtaining series solutions to a variety of linear and nonlinear differential equations of arbitrary order. Many powerful and efficient strategies have been proposed such as Laplace homotopy perturbation method [ 12 ], weighted least squares method [ 13 ], iterative method [ 14 ], homotopy perturbation Sumudu transform method [ 15 ], Elzaki transform decomposition approach [ 16 ], Laplace decomposition method [ 17 ], and natural homotopy transform method [ 18 ] with a logic sensitivity function and small diffusivity. Grzymkowski et al [ 19 ] employed HPM whereas Tripathi and Mishra [ 20 ] adopted HPM together with the Laplace transform to determine the temperature distribution in the casting-mould heterogeneous system as a continuous function, which is particularly useful for analyzing the mould.…”

Fractional Complex Transform and Homotopy Perturbation Method for the Approximate Solution of Keller-Segel Model

“…Later, various methods have been developed to show that HPM a is very efficient and powerful tool for finding the approximate solution to FDEs [15][16][17][18]. In order to get the solution of the K-S model, many powerful and efficient techniques have been suggested to obtain the analytical solutions such as Laplace homotopy perturbation method [19], iterative method [20], homotopy perturbation Sumudu transform [21], and natural homotopy transform method [22] with a logic sensitivity function and small diffusivity. Some partial differential equations with fractional order are not easy to solve, and then, their approximate solution can be evaluated.…”

Homotopy perturbation Shehu transform method for solving fractional models arising in applied sciences

“…Recently, many fractional models have been solved using analytical and numerical techniques. To mention a few, we have the homotopy perturbation method (HPM) [6], the Adomian decomposition method (ADM) [7], the Laplace decomposition method (LDM) [8], the homotopy perturbation transform method (HPTM) [9], and so on. Besides using the Laplace-type integral transform [10,11], some new efficient iterative techniques with the Caputo fractional derivative [12] and Atangana-Baleanu fractional derivative [13] are developed, for example, see [14][15][16][17][18][19][20][21][22][23][24][25].…”