Fractional Differential Equations: Theoretical Aspects and Applications presents the latest mathematical and conceptual developments in the field of Fractional Calculus and explores the scope of applications in research science and computational modeling. The book delves into these methods and applied computational modelling techniques, including analysis of equations involving fractional derivatives, fractional derivatives and the wave equation, analysis of FDE on groups, direct and inverse problems, functional inequalities, and computational methods for FDEs in physics and engineering. Other modeling techniques and applications explored include general fractional derivatives involving the special functions in analysis and fractional derivatives with respect to other functions. Fractional Calculus, the field of mathematics dealing with operators of differentiation and integration of arbitrary real or even complex order, extends many of the modelling capabilities of conventional calculus and integer-order differential equations and finds its application in various scientific areas, such as physics, mechanics, engineering, economics, finance, biology, and chemistry, among others.
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Table of Contents
1. Introduction and Overview2. Modelling Capillary Absorption in Building Materials with Emphasis on the Fourth Root Time Law
3. Fractional Velocities
4. Quintic and Quinticated Oscillators
5. Krasnoselskii-Type Theorems for Monotone Operators in Ordered Banach Algebra with Applications in Fractional Differential Equations and Inclusion
6. Computational Preconditioned Gauss-Seidel via Half-Sweep Approximation to Caputo's Time-Fractional Differential Equations
7. Congruence between Mild and Classical Solutions of Generalized Fractional Impulsive Evolution Equation
8. On the Conformable Fractional Triple Sumudu Transform and its Applications
9. Numerical Approximation of the General Model of Fractional Partial Differential
Equations Arising in Science and Engineering
10. Fractional Space of Sobolev Type with Riemann-Liouville Fractional Derivative
11. Fractional Differential Equation Model for RLC Circuits
12. Fractional Calculus-Based Dynamic Systems
13. Soliton Solution of Damped KdV Equation in Unmagnetized Superthermal
Plasmas: Application of Adomian Decomposition Method
14. (?, ?)-BVP for Impulsive Differential Equations of Fractional Order on Banach Space
15. An Optimal Control Analysis of HIV/Visceral Leishmaniasis Co-Infection Model
16. A General-Purpose Fractional Order Optimal Control Problem (FOOCP) Solver and a Benchmark on Optimal Vaccination Control of a Pandemic
Authors
Praveen Agarwal Full Professor, Anand International College of Engineering, Jaipur India; Nonlinear DynamicsResearch Center (NDRC), Ajman University, Ajman, UAE; Peoples Friendship University of Russia (RUDN University), Russian Federation.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.
Carlo Cattani Professor (habil. full professor) of Mathematical Physics and Applied Mathematics at the Engineering School (DEIM) of Tuscia University (VT), Italy. Dr. Carlo Cattani is Full Professor of Mathematical Physics and Applied Mathematics at the Department of Economics, Engineering, Society and Enterprise (DEIM) at Universit� degli Studi della Tuscia, Viterbo, Italy. He has been previously appointed as Professor and Research Fellow at the Department of Mathematics, University of Rome La Sapienza, and Department of Mathematics, University of Salerno. Dr. Cattani has been a Research Fellow at the Italian Council of Research (CNR) and Visiting Research Fellow at the Physics Institute of Stockholm University. His main scientific research interests are focused on numerical and computational methods, mathematical models and methods, time series and data analysis, computer methods and simulations. Dr. Cattani is co-author of several books, including The Natural Language for Artificial Intelligence, Elsevier Academic Press; Wavelet and Wave Analysis as Applied to Materials with Micro or Nanostructure, World Scientific Publishing; Fractional Dynamics, De Gruyter; Computational Methods for Data Analysis, De Gruyter; Fractal Analysis: Basic Concepts and Applications, World Scientific Publishing; Symmetry and Complexity, Mdpi AG; and Advances in Mathematical Modelling: Applied Analysis and Computation, Springer. He has made significant contributions to scientific and mathematical research on fundamental topics such as numerical methods, dynamical systems, fractional calculus, fractals, wavelets, nonlinear waves, and data analysis. Dr. Cattani is Editor in Chief of the journals Fractal and Fractional and Information Sciences Letters. Shaher Momani Dean, College of Humanities and Sciences, Ajman University, United Arab Emirates and Distinguished Professor of Mathematics, University of Jordan, Jordan. Dr. Shaher Momani is Dean of the College of Humanities and Sciences at Ajman University, United Arab Emirates, and Distinguished Professor of Mathematics at the University of Jordan. He has previously been Dean of Scientific Research, Dean of Faculty of Science, and Head of Department of Mathematics at The University of Jordan. Dr. Momani has received numerous academic honors in the course of his career, including among many others The Order of King Abdullah II Ibn Al Hussein for Academic Contributions in Scientific Research, Jordanian Star of Science, ISI Web of Science Highly-Cited Interdisciplinary Researcher, ISI Web of Science Highly-Cited Researcher in Mathematics, named by Clarivate Analytics as one of the World's Most Influential Scientific Minds 2014-2018, Liouville Award for Lifetime Achievement in Fractional Calculus, and the Mittag-Leffler Award for Fractional Differentiation and Its Applications. Dr. Momani has been classified as the top scientist in the world in terms of publications in fractional differential equations according to Clarivate and Scopus from 2008-2015, currently with 6959 Scopus citations. Dr. Momani is Editor in Chief of Numerical and Computational Methods in Sciences and Engineering. His research interests include Mathematical Modelling, Fractional Dynamical Systems, Numerical solution of ordinary and partial differential equations of fractional order, theory of fractional differential equations and integral equations, Newtonian and non-Newtonian fluid dynamics, stability of fractional linear systems, fractional order modelling and control in Biomedical Engineering, variational inequalities and obstacle problems, Mathematical Biology, and Mathematical Physics.
