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Fractional Derivatives with Mittag-Leffler Kernel

Trends and Applications in Science and Engineering

  • Book
  • © 2019

Overview

Editors:
  1. José Francisco Gómez

    1. CONACYT-Tecnológico Nacional de México, Centro Nacional de Investigación y Desarrollo Tecnológico, Cuernavaca, Mexico

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    You can also search for this editor in PubMed   Google Scholar

  2. Lizeth Torres

    1. CONACYT-Instituto de Ingeniería, Universidad Nacional Autónoma de México, Mexico City, Mexico

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    You can also search for this editor in PubMed   Google Scholar

  3. Ricardo Fabricio Escobar

    1. Tecnológico Nacional de México, Centro Nacional de Investigación y Desarrollo Tecnológico, Cuernavaca, Mexico

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  • Reports on cutting-edge theories and methods for fractional calculus
  • Describes applications to real-world problems
  • Shows how to model a range of physical phenomena by using differential operators with singular kernel

Part of the book series: Studies in Systems, Decision and Control (SSDC, volume 194)

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Table of contents (18 chapters)

  1. Front Matter

    Pages i-viii
    Download chapter PDF

  2. Reproducing Kernel Method for Fractional Derivative with Non-local and Non-singular Kernel

    • Ali Akgül
    Pages 1-12

  3. Necessary and Sufficient Optimality Conditions for Fractional Problems Involving Atangana–Baleanu’s Derivatives

    • G. M. Bahaa, A. Atangana
    Pages 13-33

  4. 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

  5. Modeling and Analysis of Fractional Leptospirosis Model Using Atangana–Baleanu Derivative

    • Saif Ullah, Muhammad Altaf Khan
    Pages 49-67

  6. Dual Fractional Analysis of Blood Alcohol Model Via Non-integer Order Derivatives

    • Kashif Ali Abro, J. F. Gómez-Aguilar
    Pages 69-79

  7. 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

  8. Existence and Uniqueness Results for a Novel Complex Chaotic Fractional Order System

    • Ilknur Koca, A. Atangana
    Pages 97-115

  9. On the Chaotic Pole of Attraction with Nonlocal and Nonsingular Operators in Neurobiology

    • Emile F. Doungmo Goufo, Abdon Atangana, Melusi Khumalo
    Pages 117-134

  10. Modulating Chaotic Oscillations in Autocatalytic Reaction Networks Using Atangana–Baleanu Operator

    • Emile F. Doungmo Goufo, A. Atangana
    Pages 135-158

  11. Development and Elaboration of a Compound Structure of Chaotic Attractors with Atangana–Baleanu Operator

    • Emile F. Doungmo Goufo
    Pages 159-174

  12. On the Atangana–Baleanu Derivative and Its Relation to the Fading Memory Concept: The Diffusion Equation Formulation

    • Jordan Hristov
    Pages 175-193

  13. Numerical Solutions and Pattern Formation Process in Fractional Diffusion-Like Equations

    • Kolade M. Owolabi
    Pages 195-216

  14. 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

  15. Atangana–Baleanu Derivative with Fractional Order Applied to the Gas Dynamics Equations

    • Sunil Kumar, Amit Kumar, J. J. Nieto, B. Sharma
    Pages 235-251

  16. 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

  17. 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

  18. 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

  19. 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
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Keywords

About this book

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.

Editors and Affiliations

  • CONACYT-Tecnológico Nacional de México, Centro Nacional de Investigación y Desarrollo Tecnológico, Cuernavaca, Mexico

    José Francisco Gómez

  • CONACYT-Instituto de Ingeniería, Universidad Nacional Autónoma de México, Mexico City, Mexico

    Lizeth Torres

  • Tecnológico Nacional de México, Centro Nacional de Investigación y Desarrollo Tecnológico, Cuernavaca, Mexico

    Ricardo Fabricio Escobar

Bibliographic Information

  • Book Title: Fractional Derivatives with Mittag-Leffler Kernel

  • Book Subtitle: Trends and Applications in Science and Engineering

  • Editors: José Francisco Gómez, Lizeth Torres, Ricardo Fabricio Escobar

  • Series Title: Studies in Systems, Decision and Control

  • DOI: https://doi.org/10.1007/978-3-030-11662-0

  • Publisher: Springer Cham

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: Springer Nature Switzerland AG 2019

  • Hardcover ISBN: 978-3-030-11661-3Published: 21 February 2019

  • eBook ISBN: 978-3-030-11662-0Published: 13 February 2019

  • Series ISSN: 2198-4182

  • Series E-ISSN: 2198-4190

  • Edition Number: 1

  • Number of Pages: VIII, 341

  • Number of Illustrations: 45 b/w illustrations, 42 illustrations in colour

  • Topics: Control and Systems Theory, Calculus, Numerical and Computational Physics, Simulation

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