Time-Fractional Order Biological Systems with Uncertain Parameters (Synthesis Lectures on Mathematics & Statistics)

The subject of fractional calculus has gained considerable popularity and importance during the past three decades, mainly due to its validated applications in various fields of science and engineering. It is a generalization of ordinary differentiation and integration to arbitrary (non-integer) order. The fractional derivative has been used in various physical problems, such as frequency-dependent damping behavior of structures, biological systems, motion of a plate in a Newtonian fluid, ��������λ����μ controller for the control of dynamical systems, and so on. It is challenging to obtain the solution (both analytical and numerical) of related nonlinear partial differential equations of fractional order. So for the last few decades, a great deal of attention has been directed towards the solution for these kind of problems. Different methods have been developed by other researchers to analyze the above problems with respect to crisp (exact) parameters.

However, in real-lifeapplications such as for biological problems, it is not always possible to get exact values of the associated parameters due to errors in measurements/experiments, observations, and many other errors. Therefore, the associated parameters and variables may be considered uncertain. Here, the uncertainties are considered interval/fuzzy. Therefore, the development of appropriate efficient methods and their use in solving the mentioned uncertain problems are the recent challenge.

In view of the above, this book is a new attempt to rigorously present a variety of fuzzy (and interval) time-fractional dynamical models with respect to different biological systems using computationally efficient method. The authors believe this book will be helpful to undergraduates, graduates, researchers, industry, faculties, and others throughout the globe.

Dr. Snehashish Chakraverty works in the Department of Mathematics (Applied Mathematics Group), National Institute of Technology Rourkela, Odisha, as a Senior (Higher Administrative Grade) Professor and is also the Dean of Student Welfare of the institute since November 2019. He received his Ph.D. from IIT Roorkee in 1992. Then he did post-doctoral research at ISVR, University of Southampton, U.K., and at Concordia University, Canada. He was a visiting professor at Concordia and McGill Universities, Canada, and University of Johannesburg, South Africa. Prof. Chakraverty has authored 17 books and published approximately 345 research papers in journals and conferences. He was the President of the Section of Mathematical Sciences (including Statistics) of Indian Science Congress (2015-2016) and was the Vice President―Orissa Mathematical Society (2011-2013). Prof. Chakraverty is a recipient of prestigious awards viz. INSA International Bilateral Exchange Program, Platinum Jubilee ISCA Lecture, CSIR Young Scientist, BOYSCAST, UCOST Young Scientist, Golden Jubilee CBRI Director's Award, Roorkee University gold Medals and more. He has undertaken17 research projects as Principal Investigator funded by different agencies totaling about Rs.1.6 crores. Prof. Chakraverty is the Chief Editor of International Journal of Fuzzy Computation and Modelling (IJFCM), Inderscience Publisher, Switzerland, Associate Editor of Computational Methods in Structural Engineering, Frontiers in Built Environment, and an Editorial Board member of Springer Nature Applied Sciences, IGI Research Insights Books, Springer Book Series of Modeling and Optimization in Science andTechnologies, Coupled Systems Mechanics (Techno Press), Curved and Layered Structures (De Gruyter), Journal of Composites Science (MDPI), Engineering Research Express (IOP), Applications and Applied Mathematics: An International Journal, and Computational Engineering and Physical Modeling (Pouyan Press). His present research area includes Differential Equations (Ordinary, Partial, and Fractional), Numerical Analysis and Computational Methods, Structural Dynamics (FGM, Nano), and Fluid Dynamics, Mathematical Modeling and Uncertainty Modeling, and Soft Computing and Machine Intelligence (Artificial Neural Network, Fuzzy, Interval and Affine Computations).