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Full Description
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.
Contents
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. (ω, ρ)-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
