1st Edition

# Special Functions in Fractional Calculus and Engineering

Edited By Harendra Singh, H M Srivastava, R. K. Pandey Copyright 2023
314 Pages 80 B/W Illustrations
by CRC Press

314 Pages 80 B/W Illustrations
by CRC Press

Also available as eBook on:

Special functions play a very important role in solving various families of ordinary and partial differential equations as well as their fractional-order analogs, which model real-life situations. Owing to the non-local nature and memory effect, fractional calculus is capable of modeling many situations which arise in engineering. This book includes a collection of related topics associated with such equations and their relevance and significance in engineering.

Special Functions in Fractional Calculus and Engineering highlights the significance and applicability of special functions in solving fractional-order differential equations with engineering applications. This book focuses on the non-local nature and memory effect of fractional calculus in modeling relevant to engineering science and covers a variety of important and useful methods using special functions for solving various types of fractional-order models relevant to engineering science. This book goes on to illustrate the applicability and usefulness of special functions by justifying their numerous and widespread occurrences in the solution of fractional-order differential, integral, and integrodifferential equations.

This book holds a wide variety of interconnected fundamental and advanced topics with interdisciplinary applications that combine applied mathematics and engineering sciences, which are useful to graduate students, Ph.D. scholars, researchers, and educators interested in special functions, fractional calculus, mathematical modeling, and engineering.

Chapter 1. An Introductory Overview of Special Functions and Their Associated Operators of Fractional Calculus

H. M. Srivastava

Chapter 2. Analytical Solutions for Fluid Model Described by Fractional Derivative Operators Using Special Functions in Fractional Calculus

Ndolane Sene

Chapter 3. Special Functions and Exact Solutions for Fractional Diffusion Equations with Reaction Terms

E. K. Lenzi and M. K. Lenzi

Chapter 4. Computable Solution of Fractional Kinetic Equations Associated with Incomplete ℵ-Functions and M-Series

Nidhi Jolly and Manish Kumar Bansal

Chapter 5. Legendre Collocation Method for Generalized Fractional Advection Diffusion Equation.

Sandeep Kumar, R. K. Pandey, Shiva Sharma, Harendra Singh

Chapter 6. The Incomplete Generalized Mittag-Leﬄer Function and Fractional Calculus Operators

Rakesh K. Parmar and Purnima Chopra

Chapter 7. Numerical Solution of Fractional Order Diffusion Equation Using Fibonacci Neural Network

Kushal Dhar Dwivedi

Chapter 8. Analysis of a Class of Reaction-Diffusion Equation Using Spectral Scheme

Prashant Pandey and Priya Kumari

Chapter 9. New Fractional Calculus Results for the Families of Extended Hurwitz-Lerch Zeta Function

Rakesh K. Parmar, Arjun K. Rathie and S. D. Purohit

Chapter 10. Compact Diﬀerence Schemes for Solving the Equation of Oscillator Motion with Viscoelastic Damping

A. M. Elsayed and T. S. Aleroev

Chapter 11. Dynamics of the Dadras-Momeni System in the Frame of the Caputo-Fabrizio Fractional Derivative

Chandrali Baishya and P. Veeresha

Chapter 12. A Fractional Order Model with Non-Singular Mittag-Leffler Kernel

Ali Akgül

### Biography

Dr. Harendra Singh is an Assistant Professor at the Department of Mathematics, Post-Graduate College, Ghazipur-233001, Uttar Pradesh, India, and has been listed in the top 2% scientists list published by Stanford University. He primarily teaches subjects such as real and complex analysis, functional analysis, abstract algebra, and measure theory in post-graduate level courses in mathematics. Dr. Singh has published 50 research papers in various journals of repute and has published three books from Taylor and Francis, one with Springer and one with Elsevier. He has attained a number of national and international conferences and presented several research papers. He is a reviewer of various journals, and his areas of interest are mathematical modeling, Fractional differential equations, integral equations, calculus of variations, and analytical and numerical methods.

Dr. H. M. Srivastava is a Professor Emeritus, Department of Mathematics and Statistics, University of Victoria, British Columbia V8W 3R4, Canada. He earned his Ph.D. degree in 1965 while he was a full-time member of the teaching faculty at the Jai Narain Vyas University of Jodhpur in India (since 1963). Professor Srivastava has held (and continues to hold) numerous Visiting, Honorary and Chair Professorships at many universities and research institutes in different parts of the world. Having received several D.Sc. degrees as well as honorary memberships and fellowships of many scientific academies and scientific societies around the world, he is also actively associated editorially with numerous international scientific research journals as an Honorary or Advisory Editor or as an Editorial Board Member. He has also edited many special issues of scientific research journals as the Lead or Joint Guest Editor. He has published 36 books, monographs, and edited volumes, 36 books (and encyclopedia) chapters, 48 papers in international conference proceedings, and more than 1350 peer-reviewed international scientific research journal articles, as well as Forewords and Prefaces to many books and journals. Dr. Srivastava’s research interests include several areas of pure and applied mathematical sciences, such as real and complex analysis, fractional calculus and its applications, integral equations and transforms, higher transcendental functions and their applications, q-series and q-polynomials, analytic number theory, analytic and geometric inequalities, probability and statistics, and inventory modeling and optimization.

Dr. Rajesh Pandey is an Associate Professor in the Department of Mathematical Sciences, at the Indian Institute of Technology (BHU), Varanasi, India. He is the recipient of the Indo-US fellowship and INSA Visiting Fellowship for the year 2012. He had been a visiting faculty member at the Southern Illinois University, Carbondale Illinois, IL, during 2012-13, The University of Tokyo, Japan from Nov-Dec, 2010, Central South University China, and Shanghai University Shanghai, China in Dec. 2020. He has also worked as an Assistant Professor in Mathematics at BITS Pilani and the Indian Institute of Information Technology Design and Manufacturing Jabalpur from July 2009-May 2014. Dr. Pandey received his Ph.D. degree from the Department of Applied Mathematics, Institute of Technology (BHU), Varanasi, India in 2009 and has published 60 research papers in refereed journals and guided 8 Ph.D. students. He has been a member of management committees for academic institutions and also a member of the advisory committees in various national and international conferences. His current areas of research include fractional derivatives, image processing, and numerical methods for integral and integrodifferential equations.