Time-Fractional Order Biological Systems with Uncertain Parameters

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, 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.

Auteur

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).Rajarama Mohan Jena is currently working as a Senior Research Fellow at the Department of Mathematics, National Institute of Technology Rourkela, India. He is an INSPIRE (Innovation in Science Pursuit for Inspired Research) fellow of the Department of Science of Technology, Ministry of Science and Technology, Government of India, and doing his research under this fellowship. Rajarama does research in Fractional Dynamical Systems, Applied Mathematics, Computational Methods, Numerical Analysis, Partial Differential Equations, Fractional Differential Equations, Uncertainty Modeling, and Soft Computing, and so on. He has published 12 research papers in journals, two conference papers, and one book chapter. Rajarama has also served as a reviewer for various international journals. He has been continuing collaborative works with renowned researchers from Turkey, Canada, Iran, Egypt, Nigeria, United Kingdom, and other countries.Subrat Kumar Jena is currently working as a Research Fellow at the Department of Mathematics, National Institute of Technology Rourkela, India. He is also working in a Defence Researc hand Development Organisation (DRDO)-sponsored project entitled ""Vibrations of Functionally Graded Nanostructural Members"" in collaboration with Defence Metallurgical Research Laboratory (DMRL) Lab, Hyderabad. Subrat does research in Structural Dynamics, Nano Vibration, Applied Mathematics, Computational Methods, and Numerical Analysis, Uncertainty Modeling, Soft Computing, and other areas. He has published 16 research papers (till date) in journals, 5 conference papers, and 5 book chapters. He has also served as the reviewer for various international journals. He has been continuing collaborative research works with renowned researchers from Italy, Estonia, Turkey, Iran, Poland, and other countries.

Contenu
Preface.- Acknowledgments.- Preliminaries to Fractional Calculus.- Preliminaries of Fuzzy Set Theory.- Fuzzy Fractional Differential Equations and Method of Solution.- Imprecisely Defined Time-Fractional Model of Cancer Chemotherapy Effect.- Fuzzy Time-Fractional Smoking Epidemic Model.- Time-Fractional Model of HIV-I Infection of CD4+ T Lymphocyte Cells in Uncertain Environment.- Time-Fractional Model of Hepatitis E Virus with Uncertain Parameters.- Fuzzy Time-Fractional SIRS-SI Malaria Disease Model.- Authors' Biographies.