Generalized Fractional Order Differential Equations Arising in Physical Models

This book analyzes the various semi-analytical and analytical methods for finding approximate and exact solutions of fractional order partial differential equations. It explores approximate and exact solutions obtained by various analytical methods for fractional order partial differential equations arising in physical models.

List of Figures List of Tables List of Figures List of Tables Preface Acknowledgments Authors 1. Introduction and Preliminaries of Fractional Calculus 2. Overview of Numerous Analytical Methods 3. New Analytical Approximate Solutions of Fractional Differential Equations 4. New Analytical Approximate Solutions of Riesz Fractional Differential Equations 5. New Exact Solutions of Fractional Differential Equations by Fractional Sub-Equation and Improved Fractional Sub-Equation Method 6. New Exact Solutions of Fractional Differential Equations by (G’/G)-Expansion Method and Improved (G’/G)-Expansion Method 7. New Exact Solutions of Fractional Differential Equations by Proposed Tanh and Modified Kudryashov Methods 8. New Exact Solutions of Fractional Differential Equations by Proposed Novel Method 9. New Exact Solutions of Fractional Coupled Differential Equations by Jacobi Elliptic Function Method 10. Formulation and Solutions of Fractional Continuously Variable-Order Mass-Spring Damper Systems References Index

Dr. S. Saha Ray is currently a Professor at the Department of Mathematics, National Institute of Technology, Rourkela, India. Dr. Saha Ray completed his Ph.D. in 2008 from Jadavpur University, Kolkata, India. He received his M.C.A. degree in 2001 from Indian Institute of Engineering Science and Technology (IIEST), erstwhile Bengal Engineering College, Shibpur, India. He completed a master’s degree in applied mathematics at the Calcutta University, Kolkata, India, in 1998 and a bachelor’s (honors) degree in mathematics at St. Xavier’s College(currently known as St. Xavier’s University, Kolkata), Kolkata, India, in 1996. Dr. Saha Ray has about Seventeen years of teaching experience at the undergraduate and postgraduate levels in glorious Institutes like National Institute of Technology, Rourkela and two renowned private Engineering Institutes in Kolkata, West Bengal. He has also about Sixteen years of research experience in various fields of Applied Mathematics. He has published many peer reviewed research papers in numerous fields and various international SCI journals of repute, like Applied Mathematics and Computation, Communication in Nonlinear Science and Numerical Simulation, Nonlinear Dynamics, Transaction ASME Journal of Applied Mechanics, Journal of Computational and Nonlinear Dynamics, Computers and Mathematics with Applications, Journal of Computational and Applied Mathematics, Mathematical Methods in the Applied Sciences, Computers & Fluids, Physica Scripta, Communications in Theoretical Physics, Nuclear Engineering and Design, International Journal of Nonlinear Science and Numerical Simulation, Annals of Nuclear Energy, and Journal of Mathematical Chemistry, etc. For a detail citation overview, the reader may be referred to Scopus. To date, he has more than 149 research papers published in journals of international repute, including more than 119 SCI journal papers. Dr. S. Sahoo is currently an Assistant Professor in the Department of Mathematics, Kalinga Institute of Industrial Technology (KIIT), Bhubaneswar, India. He has done Ph. D. under the supervision of Prof. S. Saha Ray in department of Mathematics of National Institute of Technology Rourkela, Odisha, India. He has been working on the BRNS research project entitled "Application of analytical methods for the solutions of generalized fractional and continuous order differential equations with the implementation in computer simulation" funded by the BRNS, BARC, Department of Atomic Energy (DAE), Govt. of India, under the supervision of Prof. S. Saha Ray who was the Principal Investigator of the aforesaid BRNS Project. Also, he has awarded senior research fellowship (SRF) funded by CSIR. Furthermore, he has pursued M.Sc. in applied mathematics from National Institute of Technology Rourkela, Odisha, India and B.Sc. from Government Autonomous College, Rourkela, Odisha, India. His current research interest includes the analytical methods for the solution of Partial and fractional differential equations.