Recent Trends in Fractional Calculus and Its Applications (Advanced Studies in Complex Systems) - Softcover

Softcover

ISBN 10: 0443185050 ISBN 13: 9780443185052

Verlag: Academic Press, 2024

Inhaltsangabe

Recent Trends in Fractional Calculus and Its Applications addresses the answer to this very basic question: "Why is Fractional Calculus important?" Until recent times, Fractional Calculus was considered as a rather esoteric mathematical theory without applications, but in the last few decades there has been an explosion of research activities on the application of Fractional Calculus to very diverse scientific fields ranging from the physics of diffusion and advection phenomena, to control systems to finance and economics. An important part of mathematical modelling of objects and processes is a description of their dynamics.

The term Fractional Calculus is more than 300 years old. It is a generalization of the ordinary differentiation and integration to noninteger (arbitrary) order. The subject is as old as the calculus of differentiation and goes back to times when Leibniz, Gauss, and Newton invented this kind of calculation. Several mathematicians contributed to this subject over the years. People like Liouville, Riemann, and Weyl made major contributions to the theory of Fractional Calculus. In recent decades the field of Fractional Calculus has attracted the interest of researchers in several areas, including mathematics, physics, chemistry, engineering, finance, and social sciences.

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Über die Autorinnen und Autoren

Dr. Praveen Agarwal earned his Ph. D. in Mathematics at the Malviya National Institute of Technology (MNIT) in Jaipur, India, in 2006. Recently, Prof. Agarwal has been listed as the World's Top 2% Scientist from 2020-2025, released by Stanford University. In the 2025 ranking of best scientists worldwide announced by Research.com, he ranked 13th at the India level and 1297th worldwide in Mathematics. Dr. Agarwal has been actively involved in research as well as pedagogical activities for the last 24 years. His major research interests include Special Functions, Fractional Calculus, Numerical Analysis, Differential and Difference Equations, Inequalities, Probability & Statistics, and Fixed Point Theorems. He has published 11 research monographs and edited volumes and more than 405 publications (with almost 100 mathematicians all over the world) in prestigious national and international mathematics journals. Dr. Agarwal worked previously either as a regular faculty or as a visiting professor and scientist in universities in several countries, including India, Germany, Turkey, South Korea, UK, Russia, Malaysia and Thailand. He has served over 50 Journals in the capacity of an Editor/Honorary Editor, or Associate Editor, and published 15 books as an editor.

Dr. Luis Vázquez Martínez is Professor Emeritus of Applied Mathematics Departamento de Matématica Aplicada, Faculdad do Informática, Universidad Complutense de Madrid, Spain. Dr. Martínez has held many distinguished administrative positions throughout his career, including Vice-Dean of Research, External Relations and Students of Facultad de Ciencias Físicas, Academic Director of Research at UCM, and Director and Founder of the European Office of Research and the Supercomputing Center, UCM, among many others. Dr. Martínez has received many awards and research honors during his distinguished career, including the Daza Valdés Prize from the Spanish Society of Optica, Cavaliere dell’Ordine della Stella from the Republic of Italy, NASA Distinction as Principal Investigator of REMS-Curiosity-MSL, and the Liouville Award for Lifetime Achievements in the Area of Fractional Calculus and Its Applications. Dr. Martínez was a Founding Member of the Centre of Astrobiology associated with NASA in its Mars exploration program, where he founded and managed the Advanced Computer Laboratory.

Dr. Ervin K. Lenzi is Associate Professor of Physics at Universidade Estaudal de Ponta Grossa, Brazil. Dr. Lenzi has a Ph.D. in Physics from Centro Brasileiro de Pesquisas Física, and was a Postdoc Fellow in Physics at Politecnico di Torino, Italy. His research interests include Diffusive Processes, Complex Systems, and Applications of the Diffusion Equation. Dr. Lenzi is on the Editorial Board of Journal of Geophysics and Engineering, Mathematical Problems in Engineering, and Quantum Reports.

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An important part of mathematical modelling of objects and processes is a description of their dynamics. In this manner, we obtain a dynamical mathematical model, usually in the form of differential equations. In such equations, we are able to use a mathematical phenomenon, so-called "Fractional Calculus." The term Fractional Calculus is more than 300 years old. It is a generalization of the ordinary differentiation and integration to noninteger (arbitrary) order. The subject is as old as the calculus of differentiation and goes back to times when Leibniz, Gauss, and Newton invented this kind of calculation. Several mathematicians contributed to this subject over the years. People like Liouville, Riemann, and Weyl made major contributions to the theory of Fractional Calculus. In recent decades the field of Fractional Calculus has attracted the interest of researchers in several areas, including mathematics, physics, chemistry, engineering, and even finance and social sciences. Recent Trends in Fractional Calculus and Its Applications addresses the answer to this very basic question: "Why is Fractional Calculus important?" Until recent times, Fractional Calculus was considered as a rather esoteric mathematical theory without applications, but in the last few decades there has been an explosion of research activities on the application of Fractional Calculus to very diverse scientific fields ranging from the physics of diffusion and advection phenomena, to control systems to finance and economics. Indeed, at present, applications and/or activities related to Fractional Calculus have appeared in at least the following fields:

• Dynamical systems based upon Fractional Calculus;
• Operators of Fractional Calculus and their applications;
• Fractional-order ODEs and PDEs;
• Fractional Calculus and its applications;
• Fractional-order integro-differential equations;
• Fixed point theory and monotone operator theory;
• fractional differential equations;
• Fractional integrals and fractional derivatives associated with special functions of mathematical physics;
• Inequalities and identities involving fractional integrals and fractional derivatives;
• Fractional control of engineering systems;
• Advancement of Calculus of Variations and Optimal Control to fractional dynamic systems;
• Analytical and numerical tools and techniques;
• Fundamental explorations of the mechanical, electrical, and thermal constitutive relations and other properties of various engineering materials such as viscoelastic polymers, foams, gels, and animal tissues, and their engineering and scientific applications;
• Fundamental understanding of wave and diffusion phenomenon, their measurements and verifications, including applications to plasma physics (such as diffusion in Tokamak).

Details zur Ausgabe

• Verlag: Academic Press
• Erscheinungsdatum: 2024
• Sprache: Englisch
• ISBN 10: 0443185050
• ISBN 13: 9780443185052
• Einband: Taschenbuch
• Auflage: 1
• Anzahl der Seiten: 300
• Herausgeber: Agarwal
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