Fractional calculus is used to model many real-life situations from science and engineering. The book includes different topics associated with such equations and their relevance and significance in various scientific areas of study and research. In this book readers will find several important and useful methods and techniques for solving various types of fractional-order models in science and engineering. The book should be useful for graduate students, PhD students, researchers and educators interested in mathematical modelling, physical sciences, engineering sciences, applied mathematical sciences, applied sciences, and so on.
This Handbook:
Provides reliable methods for solving fractional-order models in science and engineering.
Contains efficient numerical methods and algorithms for engineering-related equations.
Contains comparison of various methods for accuracy and validity.
Demonstrates the applicability of fractional calculus in science and engineering.
Examines qualitative as well as quantitative properties of solutions of various types of science- and engineering-related equations.
Readers will find this book to be useful and valuable in increasing and updating their knowledge in this field and will be it will be helpful for engineers, mathematicians, scientist and researchers working on various real-life problems.
| Preface |
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vii | |
| Editors |
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xi | |
| Contributors |
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xiii | |
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1 Analytical and Numerical Methods to Solve the Fractional Model of the Vibration Equation |
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1 | (26) |
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2 Analysis of a Nonlinear System Arising in a Helium-Burning Network with Mittag-Leffler Law |
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27 | (22) |
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3 Computational Study of Constant and Variable Coefficients Time-Fractional PDEs via Reproducing Kernel Hilbert Space Method |
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49 | (30) |
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4 Spectral Collocation Method Based Upon Special Functions for Fractional Partial Differential Equations |
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79 | (24) |
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5 On the Wave Properties of the Conformable Generalized Bogoyavlensky-Konopelchenko Equation |
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103 | (18) |
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6 Analytical Solution of a Time-Fractional Damped Gardner Equation Arising from a Collisional Effect on Dust-ion-acoustic Waves in a Dusty Plasma with Bi-Maxwellian Electrons |
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121 | (30) |
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7 An Efficient Numerical Algorithm for Fractional Differential Equations |
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151 | (18) |
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8 Generalization of Fractional Kinetic Equations Containing Incomplete I-Functions |
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169 | (18) |
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9 Behavior of Slip Effects on Oscillating Flows of Fractional Second-Grade Fluid |
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187 | (18) |
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10 A Novel Fractional-Order System Described by the Caputo Derivative, Its Numerical Discretization, and Qualitative Properties |
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205 | (36) |
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11 Extraction of Deeper Properties of the Conformable Gross-Pitaevskii Equation via Two Powerful Approaches |
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241 | (30) |
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12 New Fractional Integrals and Derivatives Results for the Generalized Mathieu-Type and Alternating Mathieu-Type Series |
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271 | (28) |
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| Index |
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299 | |
Dr. Harendra Singh is an Assistant Professor in the Department of Mathematics, Post-Graduate College, Ghazipur-233001, Uttar Pradesh, India. He holds a Ph.D. in Mathematics from Indian Institute of Technology (BHU), Varanasi, India. He has qualified GATE, JRF and NBHM in Mathematics. He is also awarded by post-doctoral fellowship (PDF) in Mathematics from National Institute of Science Education and Research (NISER) Bhubaneswar Odisha, India. His research is widely published. He edited, "Methods of Mathematical Modelling Fractional Differential Equations," published by CRC Press.
Dr. H. M. Srivastava is a Professor Emeritus, Department of Mathematics and Statistics, University of Victoria, British Columbia V8W 3R4, Canada. He holds a Ph.D. from Jai Narain Vyas University of Jodhpur in India. He has held numerous Visiting, Honorary and Chair Professorships at many universities and research institutes in dierent parts of the world. He is also actively associated with numerous international journals as an Professor Srivastavas research interests include several areas of pure and applied mathematical sciences. He has published 36 books and more than 1350 peer-reviewed journal articles.
Dr. Juan J. Nieto is a Professor, University of Santiago de Compostela, ES-15782 Santiago de Compostela, Spain. Professor Nietos research interests include several areas of pure and applied mathematical sciences. He has published many books, monographs, and edited volumes, and more than 650 peer-reviewed international scientic research journal articles. Professor Nieto has held numerous Visiting and Honorary Professorships. He is also actively associated editorially with numerous journals.
