Advancing Mathematical Physics: Insights into Solving Nonlinear Time-Fractional Equations
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Ming Li [2] ; Wei Zhang [2] ; Raghda A. M. Att [3] ; Suleman H. Alfalqi [1] ; Jameel F. Alzaidi [1] ; Mostafa M. A. Khater [4]
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[1] King Khalid University
King Khalid University
Arabia Saudí
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[2] Shandong Qihong Engineering Construction Co
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[3] Xuzhou Medical University
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[4] Xuzhou Medical University & Obour High Institute for Engineering and Technolog
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- Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 4, 2024
- Idioma: inglés
- Enlaces
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Resumen
This study is centered on addressing the complexities of the nonlinear time-fractional Harry Dym equation through a combined application of analytical and numerical methodologies. The principal objective is to establish a comprehensive framework for solving this intricate fractional partial differential equation. The introduction of the Khater II method as an analytical technique presents a novel approach specifically designed to handle such equations. In tandem, the utilization of numerical schemescubic-B-spline, quantic-B-spline, and septic-B-spline methods-further refines the accuracy and efficiency of the solutions. The outcomes underscore the efficacy of these proposed methods in effectively resolving the challenges posed by the Harry Dym equation. Emphasis is placed on the dual facets of analytical insights and numerical precision. The significance of this study lies in its contribution to advancing comprehension of nonlinear time-fractional equations while offering practical tools for their resolution. The conclusions drawn from this research provide valuable insights into the practical applicability of the Khater II method and B-spline schemes in navigating complex mathematical models. The novelty of this work lies in the amalgamation of an innovative analytical approach with established numerical techniques, signifying a noteworthy contribution to this field of study.
