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.
1. New Directions in Fractional Differential Equations
2. On Riesz Derivative Problems
3. Some Proposals for a Renewal in the Field of Fractional Behaviour Studies
4. The Origin of the Generalized Memory: Analysis of the Balance Equations
and Corrections to Newtons 3rd Law
5. Modeling COVID-19 Pandemic Outbreak Using Fractional-Order Systems
6. Damage and Fatigue Described by a Fractional Model
7. Wavelet Fractional Operators
8. Fractional Calculus Applied to Image Processing
9. Dynamics, Simulation and Parameter Estimation of a Fractional
Incommensurate Model Predicting Covid-19
10. Fractional Calculus and Its Applications to Biology
11. Fractional Differential Equations and its Applications in Circuits
Theory
12. Fractional Calculus: A Reliable Tool for Solving Real World Problems
13. Approximation of Mild Solutions of a Semilinear Fractional Differential
Equation
14. Extended Fractional Calculus
15. Fractional Calculi on Time Scales
Dr. Praveen Agarwal is Vice-Principal and Professor at Anand International College of Engineering, Jaipur, India. He is listed as the World's Top 2% Scientist in 2020, 2021, 2022, and 2023, released by Stanford University. In the 2023 ranking of best scientists worldwide announced by Research.com, he ranked 21st at the India level and 2436th worldwide in Mathematics. He is a Managing Editor of Book seriesMathematics for Sustainable Developments, Springer Nature,and Editor ofBook series Mathematical Modelling & Computational Method for Innovation, Taylor & Francis Group.
He published more than 350 papers in international reputed Journals.
Dr. Luis Vįzquez Martķnez is Professor Emeritus of Applied Mathematics Departamento de Matématica Aplicada, Faculdad do Informįtica, Universidad Complutense de Madrid, Spain. Dr. Martķnez has held many distinguished administrative positions throughout his career, including Vice-Dean of Research, External Relations and Students of Facultad de Ciencias Fķsicas, 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. Martķnez has received many awards and research honors during his distinguished career, including the Daza Valdés Prize from the Spanish Society of Optica, Cavaliere dellOrdine 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. Martķnez 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 Fķsica, 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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