Affiliation:
1. GUMUSHANE UNIVERSITY
2. GUMUSHANE UNIVERSITY, TORUL VOCATIONAL SCHOOL
Abstract
This research utilizes two novel methods, specifically the conformable q-homotopy analysis transform method (Cq-HATM) and the conformable Elzaki Adomian decomposition method (CEADM), to examine the numerical solutions for the conformable time-fractional coupled Jaulent-Miodek system. One of the two unique methods proposed is the Cq-HATM, which is a hybrid approach that combines the q-homotopy analysis transform method with the Laplace transform, employing the concept of conformable derivative. The CEADM method, similar to the aforementioned approach, is a hybrid technique that combines the Adomian decomposition method with Elzaki transform through the utilization of the concept of conformable derivative. The computer simulations were performed to offer validation for the effectiveness and dependability of the suggested approaches. After conducting a comparison between the exact solutions and the solutions acquired using the unique methods, it is apparent that both of these approaches demonstrate simplicity, effectiveness, and competency in tackling nonlinear conformable time-fractional coupled systems.
Publisher
Anadolu Universitesi Bilim ve Teknoloji Dergisi-A: Uygulamali Bilimler ve Muhendislik
Reference45 articles.
1. [1] Liouville J. 1832. Mémoire sur quelques questions de géométrie et de mécanique, et sur un nouveau genre de calcul pour résoudre ces questions. J Ecole Polytech 1832; 13(21): 1-69.
2. [2] Miller KS, Ross B. An introduction to the fractional calculus and fractional differential equations. Wiley, New York, 1993.
3. [3] Podlubny I. Fractional Differential Equations. Academic Press, New York, 1999.
4. [4] Baleanu D, Diethelm K, Scalas E, Trujillo JJ. Fractional calculus: models and numerical methods. World Scientific, London, 2012.
5. [5] Povstenko Y. 2015. Linear fractional diffusion-wave equation for scientists and engineers. Birkhäuser, Switzerland, 2015.