Mathematics

The Fundamentals of Fractional Calculus
Editors: Dharmendra Kumar Singh, PhD
Mehmet Yavuz, PhD

The Fundamentals of Fractional Calculus

In Production
Pub Date: Forthcoming March 2025
Hardback Price: $220 US | £170 UK
Hard ISBN: 9781779520135
Pages: Est. 514pp w/index
Binding Type: Hardback / ebook
Notes: 55 color and 1 b/w illustration

Fractional calculus is one of the most important divisions of theoretical and applied mathematics. This new book, The Fundamentals of Fractional Calculus, presents a wide variety of interesting technologies and practices used in fractional calculus, providing detailed insight into recent developments in and the latest research in the field of science, engineering, etc., using fractional calculus.

The result of the teaching experiences of the editors and authors to engineering and science students, the volume goes a long way in meeting the requirements of mathematics, physics, and engineering. Chapters discuss fractional calculus via generalized functions and integral transforms of pathway type; Laplace transformation of fractional integrals and derivatives; estimating the order of derivation in a fractional differential equation; a new class of integro-differential equations with non-singular differential operators; various uses of the Caputo approach; a gingerbread-man discrete system; etc. The various applications of fractional calculus are shown with examples such as for creating and/or solving epidemic models, alcoholism models, model for divorce dynamics, and more.

This book aims to give a rigorous and thorough analysis of various aspects of fractional calculus and will be helpful for scientific readers as well as researchers working in the area of fractional calculus. The book will help to establish the key steps followed in their research methodology and concept development.

CONTENTS:
Preface

1. An Outlook on Fractional Calculus via Generalized Functions and Integral Transforms of Pathway Type

Dilip Kumar

2. Laplace Transformation of Fractional Integrals and Derivatives
Min-Jie Luo and Ravinder Krishna Raina

3. Estimating the Order of Derivation in a Fractional Differential Equation
Silvia Seminara, María Inés Troparevsky, and Marcela Fabio

4. New Class of Integro-Differential Equations with Non-Singular Differential Operators
Seda Igret Araz and Abdon Atangana

5. Exact Solution of Fractional Equations
Mousa Ilie

6. Numerical Computation of Fractional Derivatives of Caputo Type
Bengt Fornberg, Cocile Piret, and Austin Higgins

7. Some Remarks on Caputo-Weighted Integrals and Applications
J. E. Nápoles-Valdes and B. Bayraktar

8. Periodicity Solutions of K-Symbol Fractional Differential Equations with Applications
Rabha W. Ibrahim

9. Gingerbread-Man Discrete System Formulated by the K-Symbol Fractional Calculus
Rabha W. Ibrahim

10. An Improved Numerical Algorithm for Solving Multi-Order Fractional Differential Equations
Zul Qar Ahamad Noor, Imran Talib, and Muhammad Bilal Riaz

11. Existence Results for Implicit (FFDEs) with Tempered Xi-HFD
R. Vivek, K. Kanagarajan, and D. Vivek

12. Computational Study of the Fractional Order of an Alcoholism Model
Yerra Shankar Rao, Binayak Dihudi, and Anasuya Nath

13. A Statistical-Oriented Application of the Erdélyikober Fractional Integral in Epidemic Model Problems
Hemant Kumar

14. A Comprehensive Qualitative Examination of a Fractional-Order Model for Divorce Dynamics
Yasir Nadeem Anjam, Mehmet Yavuz, Amna Batool, and Mati Ur Rahman

15. A Numerical Study of the Jaulent-Miodek Model Using Homotopy Perturbation Transform Technique via the Caputo-Fabrizio Operator
Amit Prakash, Ajay Kumar, and Rahul

16. Fractional Kinetic Equation with Incomplete Wright Function
Dharmendra Kumar Singh

Index


About the Authors / Editors:
Editors: Dharmendra Kumar Singh, PhD
Assistant Professor, Department of Mathematics in the School of Basic Sciences, UIET, Chhatrapati Sahau Ji Maharaja University, Kanpur, India

Dharmendra Kumar Singh, PhD, is an Assistant Professor in the Department of Mathematics in the School of Basic Sciences, UIET, Chhatrapati Sahau Ji Maharaja University, Kanpur, India. He has 12 years of research and teaching experience in the field of fractional calculus. His research interest is in special functions, fractional calculus, partial fractional differential equations, and distribution theory. Dr. Singh has published research journal papers and book chapters on fractional calculus and received the award for best publication from The Society for Special Functions and Their Applications for the year 2019. He is a reviewer for many reputed international journals. He has also attended and presented research papers at several national and international conferences and symposiums.

Mehmet Yavuz, PhD
Associate Professor, Mathematics and Computer Sciences Department, Necmettin Erbakan University, Türkiye

Mehmet Yavuz, PhD, is currently an Associate Professor in the Mathematics and Computer Sciences Department, Necmettin Erbakan University, Türkiye. He has published more than 85 research papers in reputed journals and 60 conference papers as well as several book chapters in international books. He edited a book titled Fractional Calculus: New Applications in Understanding Nonlinear Phenomena, published by Bentham Science Publishing. He has received an award for being the most published scientist with international cooperation scientists (gold medal) and two awards on being most published scientist in the field of science/engineering for his outstanding research work in the field of science. His research interests lie in biomathematics, infectious disease dynamics, population dynamics, stochastic analysis, calcium dynamics, fractional mathematical models, fractional mathematical theory and methods, bifurcation analysis, and dynamical control theory. Apart from being an associate editor for several esteemed journals, he is the Editor-in-Chief of the journal Mathematical Modelling and Numerical Simulation with Applications and the Dr. Yavuz received his BSc degree from Zonguldak Bulent Ecevit University, Türkiye, and both his MSc and PhD degrees in Applied Mathematics from Balýkesir University, Türkiye. He visited the Department of Mathematics at the University of Exeter, UK, for postdoctoral research.




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