Mathematics

Semi-Analytical and Numerical Approximations of Fractional Partial Differential Equations
Editors: Geeta Arora, PhD
Mamta Kapoor, PhD

Semi-Analytical and Numerical Approximations of Fractional Partial Differential Equations

In Production
Pub Date: Forthcoming November 2026
Hardback Price: $190 USD | £150 UK
Hard ISBN: 9781779645715
E-Book ISBN: 978-1-77964-572-2
Pages: Est. 276 pp w index
Binding Type: Hardback / ebook
Notes: 17 color and 21 b/w illustrations

Fractional calculus, a generalization of classical calculus to arbitrary order, has emerged as a powerful tool for modeling complex phenomena across diverse scientific and engineering disciplines. Its ability to capture memory effects and non-local interactions makes it particularly well-suited for describing systems that exhibit anomalous diffusion, viscoelasticity, and other non-standard behaviors. This new book, Semi-Analytical and Numerical Approximations of Fractional Partial Differential Equations, provides a comprehensive overview of the latest advancements in the analytical and numerical techniques for solving fractional partial differential equations (FPDEs).

The book explores a wide range of applications, demonstrating the versatility and significance of fractional calculus in addressing real-world problems. From the foundational evolution of fractional calculus in modern science and technology to the specific implementations in financial modeling, fluid dynamics, epidemiology, and cryptography, the book offers a rich tapestry of theoretical insights and practical solutions.

First beginning with a historical perspective of fractional calculus and its impact in modern science and technology, the volume then delves into analytical solutions of FPDEs, showcasing the application of powerful techniques like the Yang transform and novel analytical methods for solving fractional Black-Scholes and Burgers equations. The focus then shifts to numerical approximations, presenting diverse methods for solving fractional telegraph equations, smoking models, and Lane-Emden type equations, highlighting the importance of robust and efficient numerical schemes in handling the complexities of FPDEs.

Further exploring the applications of fractional calculus, the book examines the controllability and stability of fractional systems, with a particular emphasis on digital cryptography. The fractional dispersive Korteweg–De Vries (KdV) equations are demonstrated, and the role of fractional calculus in modeling biological systems, using the Oropouche virus as an example, is showcased.

Intended for researchers, graduate students, and practitioners in mathematics, physics, engineering, and related fields who seek a comprehensive understanding of the theoretical foundations and practical applications of fractional calculus, this book highlights the cutting-edge research and the diverse approaches employed in solving FPDEs.

CONTENTS:
Preface

1. The Evolution of Fractional Calculus and Its Impact in Modern Science and Technology
Geeta Arora, Adarsh Bhardwaj, and Mahmood Khalid Jasim

2. Analytical Solution of Fractional Black-Scholes European Option Pricing Equation by Yang Transform in the Caputo Sense
Mamta Kapoor

3. Analytical Approach to Solve Time-Fractional Burgers’ Equation with Proportional Delay Argument via a Novel Technique
Saloni Agrawal and Brajesh Kumar Singh

4. A Study on Numerical Investigation of Fractional Telegraph Equations
S. Priyadharsini and E. Vignesh

5. A Numerical Study of a Smoking Model with Caputo-Fabrizio Fractional Derivative
Keerthana G, Bharathi G. S., and Sagithya Thirumalai

6. A Robust Compact Finite Difference Method for Time Fractional Burgers Equation
Ravneet Kaur, Geeta Arora, and V. K. Kukreja

7. A Computational Approach for Solving Singular Fractional Lane-Emden Type
Yogeshwari F. Patel

8. Semi-Analytical and Numerical Approaches to Trajectory Controllability of Conformable Fractional Systems of Order 1 ? ? ? 2
Vishant Shah, K. Anukiruthika, Jaita Sharma, P. Muthukumar, and Gargi Trivedi

9. Stability Analysis and Synchronization of Fractional Order System: An Application to Digital Cryptography
Ishu, Geeta and Ejaz Sabir Lone

10. Series Solution of Fractional Dispersive Korteweg-De Vries (KdV) via Yang Homotopy Perturbation Method
Geeta Arora and Mamta Kapoor

11. A Mathematical Framework for Oropouche Virus Dynamics Using Fractional Calculus
Usharani Bhimavarapu

Index


About the Authors / Editors:
Editors: Geeta Arora, PhD
Professor, Department of Mathematics, Lovely Professional University, Punjab, India

Geeta Arora, PhD, has over 12 years of teaching experience and is working as a Professor in the Department of Mathematics at Lovely Professional University, Punjab, India. She has published over 70 research papers (Scopus indexed) in both international and national journals. She has authored book chapters in national and international publications and has published books with national publishers along with several ongoing books with national and international publishers. She has conducted several workshops on MATLAB and Vedic mathematics for students and faculty members within and outside the university campus. She has supervised nine PhD scholars and is currently guiding six PhD scholars. Dr. Arora has received research appreciation awards from Lovely Professional University, Punjab, India. Dr. Arora earned her PhD degree from IIT Roorkee, India.

Mamta Kapoor, PhD
Associate Professor, Marwadi University Research Center, Department of Mathematics, Faculty of Engineering & Technology, Marwadi University, Rajkot, Gujarat, India

Mamta Kapoor, PhD, is working as an Associate Professor at the Marwadi University Research Center, Department of Mathematics, Faculty of Engineering & Technology, Marwadi University, Rajkot, Gujarat, India. She has over ten years of teaching experience and has published over 50 Scopus-indexed papers in journals of international repute. Her areas of research are numerical and analytical solutions of partial differential equations, fractional differential equations, fuzzy differential equations, and machine learning techniques in mathematics. Dr. Kapoor earned her PhD degree from Lovely Professional University, Punjab, India.




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