Fractional differential equations : theoretical aspects and applications /

This book is a scholarly work that explores theoretical aspects and applications of fractional differential equations in complex systems. Edited by Praveen Agarwal and other contributors, it provides comprehensive coverage on the extension of M-fractional derivatives, properties of Apostol-type poly...

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Bibliographic Details
Corporate Author:	ScienceDirect (Online service)
Other Authors:	Agarwal, Praveen
Format:	eBook
Language:	English
Published:	[S.l.] : Academic Press, 2024.
Subjects:	Fractional differential equations. Équations différentielles fractionnaires. Electronic books.
Online Access:	Connect to the full text of this electronic book

Table of Contents:

6.3 Spline approximation method for a system of fractional differential equations
6.3.1 Error estimation and convergence analysis
6.3.2 Stability of the method
6.3.3 Numerical example of a system of fractional differential equations
6.4 Modified homotopy perturbation method for the fractional Bagley-Torvik equation
6.4.1 Different approaches towards new iterative methods
6.4.1.1 First approach
6.4.1.2 Second approach
6.4.2 One-Step New Iterative Method (OSNIM)
6.4.3 Convergence and error analysis
6.4.4 Illustrating examples
6.5 Conclusion
References
7 A study on the properties of new generalized special functions, their integral transformations, and applications to fracti...
7.1 Introduction and preliminaries
7.2 New generalized special functions
7.3 Properties
7.4 Integral transforms
7.4.1 Beta transform
7.4.2 Mellin transform
7.4.3 Laplace transform
7.4.4 Sumudu transform
7.4.5 Elzaki transform
7.4.6 General integral transform
7.5 Solution of fractional differential equations
7.6 Conclusion
References
8 Congruence between mild and classical solutions of generalized fractional impulsive evolution equation
8.1 Introduction and preliminaries
8.2 Mild solution
8.3 Classical solution
8.4 Congruence between classical and mild solutions
References
9 Application of various methods to solve some fractional differential equations in different fields
9.1 Introduction
9.2 Preliminaries
9.3 Idea of the used methods
9.3.1 Analysis of the GMLFM
9.3.2 Analysis of the PCM
9.3.3 Analysis of the MGMLFM
9.3.4 Analysis of the LADM
9.4 Results and discussion
9.4.1 Fractional-order model of human liver
9.4.1.1 Qualitative analysis of the solution
9.4.1.2 Simulation results
9.4.2 Fractional dynamics of a predator-prey system.
9.4.2.1 Stability of the EPs
9.4.2.2 Implementing the MGMLFM and simulating the results
9.4.3 Fractional-order Broer-Kaup (BK) system
9.4.3.1 Implementation of proposed methods
9.4.3.2 Simulation of the results
9.4.4 Fractional-order Burgers' system
9.4.4.1 Implementation of proposed methods
9.4.4.2 Simulation of the results
9.5 Conclusion
References
10 Modeling capillary absorption in building materials with emphasis on the fourth root time law: time-fractional models, so...
10.1 Introduction
10.1.1 Experimental background
10.1.2 Existing models
10.1.3 Aim
10.1.4 Main lines of development of this study
10.2 New approach: physical and modeling background
10.2.1 Mass balance of absorbing species
10.2.2 Sharp front diffusion approach
10.2.3 Integral-balance solution
10.3 Next study tasks
10.4 A variety of alternative models
10.4.1 Integer-order nonlinear diffusion models
10.4.1.1 Diffusion model with a power-law time-dependent diffusivity
10.4.1.2 Fourth-order diffusion model with a constant diffusivity
10.4.2 Fractional diffusion models
10.4.2.1 Fractional diffusion model 1: constant diffusivity
10.4.2.2 Fractional diffusion model 2: time-dependent diffusivity
10.4.2.3 Fractional diffusion model 3: concentration dependent (power-law) diffusivity
10.5 Some briefs and preliminarily analyses
10.5.1 Integer-order diffusion models
10.5.1.1 Integer-order diffusion model with a time-dependent diffusivity
10.5.1.2 Fourth-order diffusion model
10.5.2 Fraction diffusion models
10.5.2.1 Fractional diffusion model 1
10.5.2.2 Fractional diffusion model 2
10.5.2.3 Fractional diffusion model 3
10.6 Tests with published data: does the 1/4 law is obeyed everywhere?
10.7 Concentration profiles: approximate solutions.
10.8 The parameter m and the exponent n in the nonlinear diffusion model: some suggestions
10.9 Conclusions
Acknowledgments
References
11 Fuzzy fractional Caputo-type numerical scheme for solving fuzzy nonlinear equations
11.1 Introduction
11.2 Construction of fuzzy fractional Newton-type numerical schemes
11.3 Numerical results
11.4 Conclusion
References
12 Approximate solutions of epidemic model of Zika virus
12.1 Introduction
12.2 Preliminaries on fractional calculus
12.3 Mathematical model formulation
12.3.1 Classical integer model
12.3.2 Fractional order mathematical model
12.4 Basic properties of the model
12.4.1 Existence and uniqueness
12.4.2 Invariant region and attractivity
12.4.3 Positivity and boundedness
12.5 Analysis
12.5.1 Equilibrium analysis
12.5.2 Stability analysis
12.5.2.1 Stability of DFE point E0
12.5.2.2 Stability of EE point E∗
12.6 Numerical methods and simulations
12.7 Numerical simulation and sensitivity analysis
12.8 Convergence analysis
12.9 Discussion
12.10 Conclusion
References
13 On the nonlocal boundary value problem for the coupled system
13.1 Introduction
13.2 Existence of solution
13.2.1 Integral condition
13.3 Uniqueness of solution
13.4 Continuous dependence
13.5 Both analytical and numerical approaches
13.5.1 The Adomian decomposition method
13.5.2 Numerical technique derivation
13.6 Numerical examples
13.7 Conclusion
References
14 Solutions of nonlinear time fractional Klein-Gordon equations using composite fractional derivatives
14.1 Introduction
14.2 Basic tools
14.2.1 Fractional calculus
14.2.2 Generalized iterative method
14.3 Solution of nonlinear fractional Klein-Gordon equations with composite fractional derivatives
14.4 Applications
14.5 Conclusion.