Fractional Differential Equations
Theoretical Aspects and Applications
Advanced Studies in Complex Systems Series

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.

1. Introduction and Overview
2. 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

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. Carlo Cattani is Full Professor of Mathematical Physics and Applied Mathematics at the Department of Economics, Engineering, Society and Enterprise (DEIM) at Università 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 scien