Comparative study of fractional Newell–Whitehead–Segel equation using optimal auxiliary function method and a novel iterative approach
Source abstract
Abstract
This research explores the solution of the time-fractional Newell–Whitehead–Segel equation using two separate methods: the optimal auxiliary function method and a new iterative method. The Newell–Whitehead–Segel equation holds significance in modeling nonlinear systems, particularly in delineating stripe patterns within two-dimensional systems. Employing the Caputo fractional derivative operator, we address two case study problems pertaining to this equation through our proposed methods. Comparative analysis between the numerical results obtained from our techniques and an exact solution reveals a strong alignment. Graphs and tables illustrate this alignment, showcasing the effectiveness of our methods. Notably, as the fractional orders vary, the results achieved at different fractional orders are compared, highlighting their convergence toward the exact solution as the fractional order approaches an integer. Demonstrating both interest and simplicity, our proposed methods exhibit high accuracy in resolving diverse nonlinear fractional order partial differential equations.
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Research context
OpenAlex topics: Fractional Differential Equations Solutions · Mathematical Biology Tumor Growth · Mathematical and Theoretical Epidemiology and Ecology Models
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
College of Foreign Studies, Shandong Technology and Business University 1 , Yantai 264005, China
Department of Mathematics, Abdul Wali Khan University 2 , Mardan 23200, Pakistan
Department of Basic Science, College of Science and Theoretical Studies, Saudi Electronic University 3 , Riyadh 11673, Saudi Arabia
Department of Computer Science and Mathematics, Lebanese American University 4 , Beirut, Lebanon
Department of Mathematics, Art and Science Faculty, Siirt University 5 , 56100 Siirt, Türkiye
Department of Mathematics, Mathematics Research Center, Near East University 6 , Near East Boulevard, PC: 99138 Nicosia /Mersin 10, Türkiye
Department of Mathematics Education, Akenten Appiah Menka University of Skills Training and Entrepreneurship Development 7 , Kumasi, Ghana
9 Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, SIMATS, Chennai 602105, Tamilnadu, India
Department of Mathematics, College of Science, Qassim University 8 , Buraydah 51452, Saudi Arabia
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