دانلود کتاب حل عددی و کاربردهای معادلات دیفرانسیل کسری، ویرایش دوم

Over the past few decades, tremendous interest has been paid to the field of fractional calculus, which finds wide applications in physics, biology, chemistry, finance, signal and image processing, hydrology, non-Newtonian fluids, etc. Given that the analytical solution to fractional models is extremely complicated in terms of transcendental functions and analytically intractable in complex cases, numerical methods become a powerful and useful tool to handle fractional differential equations. This is the motivation for the Special Issue “Numerical Solution and Applications of Fractional Differential Equations” (NSAFDE) in the Journal of Fractal and Fractional. This issue is the 2nd Edition of NSAFDE. It received 48 submissions and produced 12 accepted and published papers, all of which were subject to a rigorous review process. This reprint is a result of these 12 collections, which cover the topics of analytical techniques, numerical methods, and the applications for fractional differential equations. Regarding the analytical techniques, the complete discriminant system method of polynomials, the traveling wave transformation, the Strang splitting algorithm, the spectral analysis method, the cones fixed point theorem, Filippov’s approach, the natural transform, the residual power series method, and the Tikhonov Regularization have been considered. The numerical methods in the collection include the mixed finite element method, the artificial boundary method, the Chebyshev spectral method, the meshless technique, the compact difference scheme, and the fast Alikhanov method. Finally, some interesting applications have been presented, such as the second-grade fluid over a semi-infinite plate, biological population dynamics, the liquid crystal model, the Hopfield neural network, the preloaded compliance system and the fractional Cauchy problem in a circular annular region. All the Guest Editors of this Special Issue are grateful to the authors for their quality contributions, to the reviewers for their valuable comments and advice, and to the administrative staff of MDPI for their support in completing this Special Issue. Special thanks go to the Section Managing Editor, Mr Ethan Zhang, for his excellent collaboration and valuable assistance.