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Recent trends in fractional calculus and its applications /

This scholarly work focuses on the recent advancements in fractional calculus and its applications within complex systems. Edited by Praveen Agarwal and other prominent mathematicians, the book provides a comprehensive overview of fractional calculus, emphasizing its role in mathematical modeling an...

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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.
Series:Advanced studies in complex systems
Subjects:
Fractional calculus.
Dérivées fractionnaires.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • 4.4.1 Variable-order Riemann-Liouville pseudo-operational matrix of fractional-order Fibonacci wavelets
  • 4.4.1.1 Fractional-order piecewise Taylor functions
  • 4.4.1.2 Transformation matrix of FFWs into FPTfs
  • 4.4.1.3 Variable-order Riemann-Liouville pseudo-operational matrix for FPTfs
  • 4.4.1.4 Variable-order Riemann-Liouville pseudo-operational matrix for FFWs
  • 4.4.2 Extra pseudo-operational matrix of fractional-order Riemann-Liouville integration for fractional-order Fibonacci wavelets
  • 4.4.2.1 Extra pseudo-operational matrix of fractional-order Riemann-Liouville integration for FPTfs
  • 4.4.2.2 Extra pseudo-operational matrix of fractional-order Riemann-Liouville integration for fractional-order Fibonacci wav...
  • 4.5 Description of the computational method
  • 4.6 Convergence analysis
  • 4.7 Numerical experiments
  • 4.8 Conclusions
  • References
  • 5 Optimization of the approximate solution of the fractional squeezing flow between two infinite plates
  • 5.1 Introduction
  • 5.2 Mathematical formulation of the problem
  • 5.3 Constructing a new family of basis functions
  • 5.3.1 The Genocchi polynomials
  • 5.3.2 The generalized Genocchi polynomials
  • 5.3.3 The operational matrices
  • 5.3.4 The function approximation
  • 5.4 Description of the method
  • 5.5 Convergence analysis of the method
  • 5.6 Numerical results
  • 5.7 Conclusions
  • Conflict of interest
  • References
  • 6 Multi-parameter generalized fractional operators and their integral transforms
  • 6.1 Introduction
  • 6.2 Basic concepts
  • 6.3 Multi-parameter generalized fractional operators
  • 6.4 Examples
  • 6.5 Conclusions
  • References
  • 7 A constructive approach to the fractional Zakharov-Kuznetsov equations of weak nonlinear acoustic ion waves in plasma
  • 7.1 Introduction
  • 7.2 Preamble
  • 7.3 Convergence and error analysis: NITHPM
  • 7.4 Constructive approach: NITHPM.
  • 7.5 Application of NITHPM
  • 7.6 Graphical result and analysis
  • 7.7 Conclusions
  • References
  • 8 Integral formula for matrix factorizations of Helmholtz equation
  • 8.1 Introduction
  • 8.2 Materials and methods
  • 8.2.1 The family of fundamental solutions of the Helmholtz equation
  • 8.2.2 Integral formulas in bounded areas
  • Declarations
  • References
  • 9 Cauchy problem for matrix factorizations of Helmholtz equation on a plane
  • 9.1 Introduction
  • 9.2 The Cauchy problem for matrix factorizations of Helmholtz equation in a two-dimensional bounded domain
  • 9.2.1 The integral formula in the type of strip
  • 9.2.2 The Cauchy problem for matrix factorizations of the Helmholtz equation in a strip-type domain
  • Declarations
  • References
  • 10 The Cauchy problem for matrix factorizations of Helmholtz equation in space
  • 10.1 Introduction
  • 10.2 The Cauchy problem for matrix factorizations of the Helmholtz equation in a three-dimensional bounded domain
  • 10.3 Integral formula in the layer-type region
  • 10.4 Regularization of the Cauchy problem for matrix factorizations of the Helmholtz equation in a layer-type domain
  • Declarations
  • References
  • 11 Modified Newton successive over-relaxation for solving Caputo fractional porous medium equations
  • 11.1 Introduction
  • 11.2 Time-fractional porous medium equation in Caputo sense
  • 11.3 Iterative method and algorithm
  • 11.4 Numerical experiment, results, and discussions
  • 11.5 Conclusions
  • References
  • 12 Fractional calculi on time scales: differentiation and integration of a function with respect to another function
  • 12.1 Introduction
  • 12.2 Preliminaries on time scales
  • 12.3 Fractional calculus on time scales of a function with respect to another function
  • Acknowledgment
  • References.
  • 13 Effective strategies to reduce transmission of certain diseases based on their fractional optimal control problems
  • 13.1 Introduction
  • 13.2 Preliminaries
  • 13.2.1 Some basic concepts of FC
  • 13.2.2 A general formulation of FOCPs
  • 13.3 Results and discussion
  • 13.3.1 Formulation of PWD model within FOCP
  • 13.3.2 Optimal control strategies for ZVD involving various transmissions
  • 13.3.3 FOCP for SIRV model with a combination of vaccination and treatment
  • 13.3.4 Prevent the risk of CHD by formulation of FOCP with fish consumption
  • 13.4 Conclusions
  • References
  • 14 Fractional Caputo-type simultaneous scheme for finding all polynomial roots
  • 14.1 Introduction
  • 14.2 Construction of fractional-type family of numerical scheme
  • 14.3 Dynamical analysis
  • 14.4 Numerical results
  • 14.5 Conclusions
  • References
  • 15 Application of modified homotopy analysis transform method to fractional modified Kawahara equation
  • 15.1 Introduction
  • 15.1.1 Fractional modified Kawahara equation
  • 15.2 Basic definitions
  • 15.3 Novel modified homotopy analysis transform method
  • 15.4 Numerical analysis of fractional Kawahara equation using MHATM
  • 15.5 Numerical result and discussion
  • 15.6 Conclusions
  • Acknowledgments
  • Funding
  • Availability of data and materials
  • Conflict of interest
  • Authors' contribution
  • References
  • Index
  • Back Cover.