The homotopy—perturbation method is employed for solving this class of equations, and the time-fractional derivatives are described in the sense of Caputo. Comparisons are made with those derived by Adomian's decomposition method, revealing that the homotopy perturbation method is more accurate and convenient than the Adomian's decomposition method.
Furthermore, the results reveal that the approximate solution continuously depends on the time-fractional derivative and the proposed method incorporating the Caputo derivatives is a powerful and efficient technique for solving the fractional differential equations without requiring linearization or restrictive assumptions.
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Communications in Theoretical Physics. Download Article PDF. An increased focus on hydrogeology and mathematical biology is evident in the new edition. Hints and solutions to selected exercises have been added to the back of the book.mail.beetsoslo.com/an-extraordinary-story.php
Nonlinear Partial Differential Equations - 1st Edition
The book emphasizes hyperbolic and parabolic problems and includes a range of applications in the following areas: biology, chemistry, porous media, biological problems, combustion and detonation, traffic flow, water waves, plug flow reactors, and heat transfer. Early chapters offer insight into how to understand problems involving phenomena, how specific equations describe evolutionary processes, and what the terms in such equations describe physically.
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When discussing wave propagination and hyperbolic problems, the text develops algorithms to solve first-order equations and highlights the concept of the weak solution. The material in the book is presented in such a manner that many of the chapters are independent, which allows for instructors' flexibility to design several courses around various topics.
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An introduction to nonlinear partial differential equations
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