Fractional Derivatives with Mittag-Leffler Kernel: Trends and Applications in Science and Engineering

Description

This book offers a timely overview of fractional calculus applications, with a special emphasis on fractional derivatives with Mittag-Leffler kernel. The different contributions, written by applied mathematicians, physicists and engineers, offers a snapshot of recent research in the field, highlighting the current methodological frameworks together with applications in different fields of science and engineering, such as chemistry, mechanics, epidemiology and more. It is intended as a timely guide and source of inspiration for graduate students and researchers in the above-mentioned areas. Front Matter ....Pages i-viii Reproducing Kernel Method for Fractional Derivative with Non-local and Non-singular Kernel (Ali Akgül)....Pages 1-12 Necessary and Sufficient Optimality Conditions for Fractional Problems Involving Atangana–Baleanu’s Derivatives (G. M. Bahaa, A. Atangana)....Pages 13-33 Variable Order Mittag–Leffler Fractional Operators on Isolated Time Scales and Application to the Calculus of Variations (Thabet Abdeljawad, Raziye Mert, Delfim F. M. Torres)....Pages 35-47 Modeling and Analysis of Fractional Leptospirosis Model Using Atangana–Baleanu Derivative (Saif Ullah, Muhammad Altaf Khan)....Pages 49-67 Dual Fractional Analysis of Blood Alcohol Model Via Non-integer Order Derivatives (Kashif Ali Abro, J. F. Gómez-Aguilar)....Pages 69-79 Parameter Estimation of Fractional Gompertz Model Using Cuckoo Search Algorithm (J. E. Solís-Pérez, J. F. Gómez-Aguilar, R. F. Escobar-Jiménez, L. Torres, V. H. Olivares-Peregrino)....Pages 81-95 Existence and Uniqueness Results for a Novel Complex Chaotic Fractional Order System (Ilknur Koca, A. Atangana)....Pages 97-115 On the Chaotic Pole of Attraction with Nonlocal and Nonsingular Operators in Neurobiology (Emile F. Doungmo Goufo, Abdon Atangana, Melusi Khumalo)....Pages 117-134 Modulating Chaotic Oscillations in Autocatalytic Reaction Networks Using Atangana–Baleanu Operator (Emile F. Doungmo Goufo, A. Atangana)....Pages 135-158 Development and Elaboration of a Compound Structure of Chaotic Attractors with Atangana–Baleanu Operator (Emile F. Doungmo Goufo)....Pages 159-174 On the Atangana–Baleanu Derivative and Its Relation to the Fading Memory Concept: The Diffusion Equation Formulation (Jordan Hristov)....Pages 175-193 Numerical Solutions and Pattern Formation Process in Fractional Diffusion-Like Equations (Kolade M. Owolabi)....Pages 195-216 Heat Transfer Analysis in Ethylene Glycol Based Molybdenum Disulfide Generalized Nanofluid via Atangana–Baleanu Fractional Derivative Approach (Farhad Ali, Muhammad Saqib, Ilyas Khan, Nadeem Ahmad Sheikh)....Pages 217-233 Atangana–Baleanu Derivative with Fractional Order Applied to the Gas Dynamics Equations (Sunil Kumar, Amit Kumar, J. J. Nieto, B. Sharma)....Pages 235-251 New Direction of Atangana–Baleanu Fractional Derivative with Mittag-Leffler Kernel for Non-Newtonian Channel Flow (Muhammad Saqib, Ilyas Khan, Sharidan Shafie)....Pages 253-268 Exact Solutions for the Liénard Type Model via Fractional Homotopy Methods (V. F. Morales-Delgado, J. F. Gómez-Aguilar, L. Torres, R. F. Escobar-Jiménez, M. A. Taneco-Hernandez)....Pages 269-291 Model of Coupled System of Fractional Reaction-Diffusion Within a New Fractional Derivative Without Singular Kernel (K. M. Saad, J. F. Gómez-Aguilar, A. Atangana, R. F. Escobar-Jiménez)....Pages 293-308 Upwind-Based Numerical Approximation of a Space-Time Fractional Advection-Dispersion Equation for Groundwater Transport Within Fractured Systems (A. Allwright, A. Atangana)....Pages 309-341