Correction: New Operational Matrices for Solving Fractional Differential Equations on the Half-Line

Abstract The objective of this paper is to present two numerical techniques for solving generalized fractional differential equations. We develop Haar wavelets operational matrices to approximate the solution of generalized Caputo–Katugampola fractional differential equations. Moreover, we introduce Green–Haar approach for a family of generalized fractional boundary value problems and compare the method with the classical Haar wavelets technique. In the context of error analysis, an upper bound for error is established to show the convergence of the method. Results of numerical experiments have been documented in a tabular and graphical format to elaborate the accuracy and efficiency of addressed methods. Further, we conclude that accuracy-wise Green–Haar approach is better than the conventional Haar wavelets approach as it takes less computational time compared to the Haar wavelet method.

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Wavelet Collocation Method for Solving Multiorder Fractional Differential Equations

Journal of Applied Mathematics ◽

10.1155/2012/542401 ◽

2012 ◽

Vol 2012 ◽

pp. 1-19 ◽

Cited By ~ 30

Author(s):

M. H. Heydari ◽

M. R. Hooshmandasl ◽

F. M. Maalek Ghaini ◽

F. Mohammadi

Keyword(s):

Differential Equations ◽

Collocation Method ◽

Fractional Differential Equations ◽

Initial Conditions ◽

General Procedure ◽

Wavelet Expansion ◽

Operational Matrices ◽

Chebyshev Wavelets ◽

Block Pulse Functions ◽

Fractional Differential

The operational matrices of fractional-order integration for the Legendre and Chebyshev wavelets are derived. Block pulse functions and collocation method are employed to derive a general procedure for forming these matrices for both the Legendre and the Chebyshev wavelets. Then numerical methods based on wavelet expansion and these operational matrices are proposed. In this proposed method, by a change of variables, the multiorder fractional differential equations (MOFDEs) with nonhomogeneous initial conditions are transformed to the MOFDEs with homogeneous initial conditions to obtain suitable numerical solution of these problems. Numerical examples are provided to demonstrate the applicability and simplicity of the numerical scheme based on the Legendre and Chebyshev wavelets.

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Solvability for fractional differential equations at resonance on the half line

Applied Mathematics and Computation ◽

10.1016/j.amc.2014.08.067 ◽

2014 ◽

Vol 247 ◽

pp. 90-99 ◽

Cited By ~ 3

Author(s):

Weihua Jiang

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Half Line ◽

At Resonance ◽

Fractional Differential

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An Integral Operational Matrix of Fractional-Order Chelyshkov Functions and Its Applications

Symmetry ◽

10.3390/sym12111755 ◽

2020 ◽

Vol 12 (11) ◽

pp. 1755

Author(s):

M. S. Al-Sharif ◽

A. I. Ahmed ◽

M. S. Salim

Keyword(s):

Differential Equations ◽

Fractional Order ◽

Fractional Differential Equations ◽

Fractional Integral ◽

Operational Matrix ◽

Operational Matrices ◽

Algebraic Equations ◽

Science And Engineering ◽

Numerical Examples ◽

Fractional Differential

Fractional differential equations have been applied to model physical and engineering processes in many fields of science and engineering. This paper adopts the fractional-order Chelyshkov functions (FCHFs) for solving the fractional differential equations. The operational matrices of fractional integral and product for FCHFs are derived. These matrices, together with the spectral collocation method, are used to reduce the fractional differential equation into a system of algebraic equations. The error estimation of the presented method is also studied. Furthermore, numerical examples and comparison with existing results are given to demonstrate the accuracy and applicability of the presented method.

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Unbounded solutions to abstract boundary value problems of fractional differential equations on a half line

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.5819 ◽

2019 ◽

Cited By ~ 2

Author(s):

Fuli Wang ◽

Yujun Cui

Keyword(s):

Differential Equations ◽

Boundary Value Problems ◽

Fractional Differential Equations ◽

Boundary Value ◽

Half Line ◽

Unbounded Solutions ◽

Abstract Boundary ◽

Fractional Differential

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Existence of solutions for a coupled system of nonlinear fractional differential equations with fractional boundary conditions on the half-line

Advances in Difference Equations ◽

10.1186/1687-1847-2013-46 ◽

2013 ◽

Vol 2013 (1) ◽

pp. 46 ◽

Cited By ~ 7

Author(s):

Yuji Liu ◽

Bashir Ahmad ◽

Ravi P Agarwal

Keyword(s):

Differential Equations ◽

Boundary Conditions ◽

Fractional Differential Equations ◽

Existence Of Solutions ◽

Coupled System ◽

Half Line ◽

Nonlinear Fractional Differential Equations ◽

Fractional Differential ◽

Fractional Boundary Conditions

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A Modified Generalized Laguerre Spectral Method for Fractional Differential Equations on the Half Line

Abstract and Applied Analysis ◽

10.1155/2013/413529 ◽

2013 ◽

Vol 2013 ◽

pp. 1-12 ◽

Cited By ~ 14

Author(s):

D. Baleanu ◽

A. H. Bhrawy ◽

T. M. Taha

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Fractional Derivatives ◽

Laguerre Polynomials ◽

Collocation Methods ◽

Half Line ◽

Caputo Fractional Derivatives ◽

Polynomial Degree ◽

Generalized Laguerre Polynomials ◽

Fractional Differential

This paper deals with modified generalized Laguerre spectral tau and collocation methods for solving linear and nonlinear multiterm fractional differential equations (FDEs) on the half line. A new formula expressing the Caputo fractional derivatives of modified generalized Laguerre polynomials of any degree and for any fractional order in terms of the modified generalized Laguerre polynomials themselves is derived. An efficient direct solver technique is proposed for solving the linear multiterm FDEs with constant coefficients on the half line using a modified generalized Laguerre tau method. The spatial approximation with its Caputo fractional derivatives is based on modified generalized Laguerre polynomialsLi(α,β)(x)withx∈Λ=(0,∞),α>−1, andβ>0, andiis the polynomial degree. We implement and develop the modified generalized Laguerre collocation method based on the modified generalized Laguerre-Gauss points which is used as collocation nodes for solving nonlinear multiterm FDEs on the half line.

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