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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.
Foreword
Preface
List of Contributors
Numerical Procedure and its Applications to the Fractional-Order Chaotic System Represented with the Caputo Derivative
A New Method of Multistage Optimal Homotopy Asymptotic Method for Solution of Fractional Optimal Control Problem
Complex Chaotic Fractional-order Finance System in Price Exponent with Control and Modeling
The Duhamel Method in Transient Heat Conduction: A Rendezvous of Classics and Modern Fractional Calculus
Oscillatory Heat Transfer Due to the Cattaneo-Hristov Model on the Real Line
Optimal Homotopy Analysis of a Nonlinear Fractional-order Model for HTLV-1 Infection of CD4  T-Cells
Behavior Analysis and Asymptotic Stability of the Traveling Wave Solution of the Kaup-Kupershmidt Equation for Conformable Derivative
Mathematical Analysis of a Rumor Spreading Model within the Frame of Fractional Derivative
A Unified Approach for the Fractional System of Equations Arising in the Biochemical Reaction without Singular Kernel
Floating Object Induced Hydro-morphological Effects in Approach Channel
Subject Index
Back Cover