A new study on the Newell-Whitehead-Segel equation with Caputo-Fabrizio fractional derivative
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Scopus EXPORT DATE: 23 October 2024 @ARTICLE{Alkan202427979, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85206008071&doi=10.3934%2fmath.20241358&partnerID=40&md5=a77794439e9a192a5acb24f24d8e152f}, affiliations = {Department of Mathematics, Faculty of Science, Fırat University, Elazığ, 23119, Turkey; Department of Computer Technologies, Torul Vocational School, Gumushane University, Gumushane, 29802, Turkey}, correspondence_address = {A. Alkan; Department of Mathematics, Faculty of Science, Fırat University, Elazığ, 23119, Turkey; email: alkanasli47@gmail.com}, publisher = {American Institute of Mathematical Sciences}, issn = {24736988}, language = {English}, abbrev_source_title = {AIMS Math.} }Abstract
In this research, we propose a new numerical method that combines with the Caputo-Fabrizio Elzaki transform and the q-homotopy analysis transform method. This work aims to analyze the Caputo-Fabrizio fractional Newell-Whitehead-Segel (NWS) equation utilizing the Caputo-Fabrizio q-Elzaki homotopy analysis transform method. The Newell-Whitehead-Segel equation is a partial differential equation employed for modeling the dynamics of reaction-diffusion systems, specifically in the realm of pattern generation in biological and chemical systems. A convergence analysis of the proposed method was performed. Two-dimensional and three-dimensional graphs of the solutions have been drawn with the Maple software. It is seen that the resulting proposed method is more powerful and effective than the Aboodh transform homotopy perturbation method and conformable Laplace decomposition method in the results. © 2024 the Author(s), licensee AIMS Press.
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https://www.scopus.com/record/display.uri?eid=2-s2.0-85206008071&origin=SingleRecordEmailAlert&dgcid=raven_sc_affil_en_us_email&txGid=fee7b710fe1927be5701601457515e49https://hdl.handle.net/20.500.12440/6332
