Editors: Mehmet Yavuz, Necati Özdemir

Series Title: Current Developments in Mathematical Sciences

Fractional Calculus: New Applications in Understanding Nonlinear Phenomena

Volume 3

eBook: US $79 Special Offer (PDF + Printed Copy): US $126
Printed Copy: US $87
Library License: US $316
ISSN: 2589-2711 (Print)
ISSN: 2589-272X (Online)
ISBN: 978-981-5051-94-0 (Print)
ISBN: 978-981-5051-93-3 (Online)
Year of Publication: 2022
DOI: 10.2174/97898150519331220101


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 for modelling 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.

Audience :

Academics interested in mathematical analysis; researchers in natural sciences and social science.


In the past few decades, fractional derivatives and integrals have been recognized as powerful modelling and simulation tools for engineering, physics, economy and other application areas. Many physical laws are expressed more accurately in terms of differential equations of arbitrary order. The fractional derivatives and integrals and their potential uses have gained a great importance, mainly since they have become powerful instruments with more accurate, efficient and successful results in mathematical modelling of several complex phenomena in numerous seemingly diverse and widespread fields of science, especially engineering, finance and biology. As the fractional dynamical systems grow, mature and develop, it is very prominent to focus on the most promising novel directions that were worked out based on the novel methods and schemes handed over recently in the field.

The key objective of this book is to focus on recent advancements and future challenges on the basic foundation and applications of the fractional derivatives and integrals in dynamical systems.

This edited book received a number of submissions and 10 of high-quality chapters were accepted. The chapters of this book have a large variety of interesting and relevant subjects, namely, fractional partial differential equations, chaotic systems and control, heat conduction, numerical algorithms, complexity and fractional calculus with power law, exponential decay law and Mittag-Leffler non-singular kernel.

Dumitru Baleanu
Department of Mathematics, Cankaya University,
06530 Balgat, Ankara, Turkey
Institute of Space Sciences, R76900 Magurele-Bucharest, Romania


Jordan Hristov
Department of Chemical Engineering,
University of Chemical Technology and Metallurgy,
8 Kliment Ohridsky Blvd., 1756 Sofia, Bulgaria.