Novel approach to the analysis of fifth-order weakly nonlocal fractional Schringer equation with Caputo derivative
Caputo derivative; Laplace transform; Parabolic law; q-HATM; Soliton solutions; Weakly nonlocal Schringer equation
The main goal of this study is to find solutions for the fractional model of the fifth-order weakly nonlocal Schringer equation incorporating nonlinearity of the parabolic law and external potential using a recent modification of the homotopy analysis method (HAM) called the q-homotopy analysis transform method (q-HATM). A mixture of q-HAM and Laplace transform is the projected solutions procedure. The method contributes approximate and exact (for some special cases) solutions such as the bright soliton, dark soliton, and exponential solutions. The simulation results using Mathematica package software, demonstrate that only a few terms are enough to achieve precise, effective, and reliable approximate solutions. In addition, in terms of plots for varying fractional order, the physical behavior of q-HATM solutions has been depicted and the numerical simulation is also exhibited. The results of q-HATM reveal that the projected method is competitive, reliable, and powerful for studying complex nonlinear models of fractional type. 2021 The Authors
Akinyemi L.; Nisar K.S.; Saleel C.A.; Rezazadeh H.; Veeresha P.; Khater M.M.A.; Inc M.
https://doi.org/10.1016/j.rinp.2021.104958 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85119185960&doi=10.1016%2fj.rinp.2021.104958&partnerID=40&md5=9e564e0417d1cb0579dd334e2f97443b
Akinyemi L., Department of Mathematics, Lafayette College, Easton, PA, United States; Nisar K.S., Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser, 11991, Saudi Arabia; Saleel C.A., Department of Mechanical Engineering, College of Engineering, King Khalid University, Asir-Abha, 61421, Saudi Arabia; Rezazadeh H., Faculty of Engineering Technology, Amol University of Special Modern Technologies, Amol, Iran; Veeresha P., Department of Mathematics, Christ (Deemed to be University), Bengaluru, 560029, India; Khater M.M.A., Department of Mathematics, Faculty of Science, Jiangsu University, Zhenjiang, 212013, China, Department of Mathematics, Obour High Institute For Engineering and Technology, Cairo, 11828, Egypt; Inc M., Biruni University, Department of Computer Engineering, Istanbul, Turkey, F?rat University, Science Faculty, Department of Mathematics, Elazig, 23119, Turkey, Department of Medical Research, China Medical University Hospital, China Medical University Taichung, Taiwan