FRACTIONAL CALCULUS : new applications in understanding nonlinear phenomena

In the last two decades, many new fractional operators have appeared, often defined using integrals with special functions in the kernel as well as their extended or multivariable forms. Modern operators in fractional calculus have different properties which are comparable to those of classical operators.These have been intensively studied formodelling and analysing real-world phenomena. There is now a growing body of research on new methods to understand natural occurrences and tackle different problems. This book presents ten reviews of recent fractional operators split over three sections: 1. Chaotic Systems and Control (covers the Caputo fractional derivative, and a chaotic fractional-order financial system)2. Heat Conduction (covers the Duhamel theorem for time-dependent source terms, and the Cattaneo–Hristov model for oscillatory heat transfer)3. Computational Methods and Their Illustrative Applications (covers mathematical analysis for understanding 5 real-word phenomena: HTLV-1 infection of CD4+ T-cells, traveling waves, rumor-spreading, biochemical reactions, and the computational fluid dynamics of a non-powered floating object navigating in an approach channel). This volume is a resource for researchers in physics, biology, behavioral sciences, and mathematics who are interested in new applications of fractional calculus in the study of nonlinear phenomena. Cover Title Copyright End User License Agreement Contents Foreword Preface List of Contributors Numerical Procedure and its Applications to theFractional-Order Chaotic System Represented withthe Caputo Derivative A New Method of Multistage Optimal HomotopyAsymptotic Method for Solution of FractionalOptimal Control Problem Complex Chaotic Fractional-order Finance Systemin Price Exponent with Control and Modeling The Duhamel Method in Transient HeatConduction: A Rendezvous of Classics and ModernFractional Calculus Oscillatory Heat Transfer Due to the Cattaneo-Hristov Model on the Real Line Optimal Homotopy Analysis of a NonlinearFractional-order Model for HTLV-1 Infection ofCD4+ T-Cells Behavior Analysis and Asymptotic Stability of theTraveling Wave Solution of the Kaup-KupershmidtEquation for Conformable Derivative Mathematical Analysis of a Rumor SpreadingModel within the Frame of Fractional Derivative A Unified Approach for the Fractional System ofEquations Arising in the Biochemical Reactionwithout Singular Kernel Floating Object Induced Hydro-morphologicalEffects in Approach Channel Subject Index Back Cover