Gomez J. Fractional Derivatives with Mittag-Leffler Kernel. Trends and App..2019

Textbook in PDF format

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.
Reproducing Kernel Method for Fractional Derivative with Non-local and Non-singular Kernel
Necessary and Sufficient Optimality Conditions for Fractional Problems Involving Atangana–Baleanu’s Derivatives
Variable Order Mittag–Leffler Fractional Operators on Isolated Time Scales and Application to the Calculus of Variations
Modeling and Analysis of Fractional Leptospirosis Model Using Atangana–Baleanu Derivative
Dual Fractional Analysis of Blood Alcohol Model Via Non-integer Order Derivatives
Parameter Estimation of Fractional Gompertz Model Using Cuckoo Search Algorithm
Existence and Uniqueness Results for a Novel Complex Chaotic Fractional Order System
On the Chaotic Pole of Attraction with Nonlocal and Nonsingular Operators in Neurobiology
Modulating Chaotic Oscillations in Autocatalytic Reaction Networks Using Atangana–Baleanu Operator
Development and Elaboration of a Compound Structure of Chaotic Attractors with Atangana–Baleanu Operator
On the Atangana–Baleanu Derivative and Its Relation to the Fading Memory Concept: The Diffusion Equation Formulation
Numerical Solutions and Pattern Formation Process in Fractional Diffusion-Like Equations
Heat Transfer Analysis in Ethylene Glycol Based Molybdenum Disulfide Generalized Nanofluid via Atangana–Baleanu Fractional Derivative Approach
Atangana–Baleanu Derivative with Fractional Order Applied to the Gas Dynamics Equations
New Direction of Atangana–Baleanu Fractional Derivative with Mittag-Leffler Kernel for Non-Newtonian Channel Flow
Exact Solutions for the Liénard Type Model via Fractional Homotopy Methods
Model of Coupled System of Fractional Reaction-Diffusion Within a New Fractional Derivative Without Singular Kernel
Upwind-Based Numerical Approximation of a Space-Time Fractional Advection-Dispersion Equation for Groundwater Transport Within Fractured Systems