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 ��������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 life applications 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. 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.