Zuhur Alqahtani¹, Ahmed Eissa Hagag²

Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, Vol.39, No.4, pp. 1-15, 2023, DOI:10.23967/j.rimni.2023.10.003 - 25 October 2023

Abstract This article introduces and illustrates a novel approximation to the compound KdV-Burgers equation. For such a challenge, the q-homotopy analysis transform technique (q-HATM) is a potent approach. The suggested procedure avoids the complexity seen in many other methods and provides an approximation that is extremely near to the exact solution. The uniqueness theorem and convergence analysis of the expected problem are explored with the aid of Banach's fixed-point theory. Through a difference in the fractional derivative, the normal frequency for the fractional solution to this issue changes. All of the discovered solutions are illustrated in More >

P. Veeresha¹, Esin Ilhan², D. G. Prakasha³, Haci Mehmet Baskonus⁴, Wei Gao^5,*

CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.3, pp. 1013-1036, 2021, DOI:10.32604/cmes.2021.014988 - 24 May 2021

Abstract In this paper, we analyze the behaviour of solution for the system exemplifying model of tumour invasion and metastasis by the help of q-homotopy analysis transform method (q-HATM) with the fractional operator. The analyzed model consists of a system of three nonlinear differential equations elucidating the activation and the migratory response of the degradation of the matrix, tumour cells and production of degradative enzymes by the tumour cells. The considered method is graceful amalgamations of q-homotopy analysis technique with Laplace transform (LT), and Caputo–Fabrizio (CF) fractional operator is hired in the present study. By using the More >