Journal ArticleDOI
A new operational matrix based on Bernoulli wavelets for solving fractional delay differential equations
TLDR
This operational matrix is utilized to transform the problem to a set of algebraic equations with unknown Bernoulli wavelet coefficients, and upper bound for the error of operational matrix of the fractional integration is given.Abstract:
In this research, a Bernoulli wavelet operational matrix of fractional integration is presented Bernoulli wavelets and their properties are employed for deriving a general procedure for forming this matrix The application of the proposed operational matrix for solving the fractional delay differential equations is explained Also, upper bound for the error of operational matrix of the fractional integration is given This operational matrix is utilized to transform the problem to a set of algebraic equations with unknown Bernoulli wavelet coefficients Several numerical examples are solved to demonstrate the validity and applicability of the presented techniqueread more
Citations
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Journal ArticleDOI
Müntz-Legendre wavelet operational matrix of fractional-order integration and its applications for solving the fractional pantograph differential equations
TL;DR: A family of piecewise functions is proposed, based on which the fractional order integration of the Müntz-Legendre wavelets are easy to calculate, and this operational matrix with the collocation points is used to reduce the under study problem to a system of algebraic equations.
Journal ArticleDOI
A numerical scheme based on Bernoulli wavelets and collocation method for solving fractional partial differential equations with Dirichlet boundary conditions
Journal ArticleDOI
Fractional-order Bernoulli functions and their applications in solving fractional FredholemVolterra integro-differential equations
TL;DR: In this paper, a new set of functions called fractional-order Bernoulli functions (FBFs) were defined to obtain the numerical solution of linear and nonlinear fractional integro-differential equations.
Journal ArticleDOI
Chebyshev spectral methods for multi-order fractional neutral pantograph equations
S. S. Ezz-Eldien,S. S. Ezz-Eldien,Y. Wang,Mohamed A. Abdelkawy,Mohamed A. Abdelkawy,Mahmoud A. Zaky,A. A. Aldraiweesh,J. A. Tenreiro Machado +7 more
TL;DR: In this article, the spectral tau and collocation methods are applied to delay multi-order fractional differential equations with vanishing delay, where the fractional derivatives are described in the Caputo sense.
References
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Book
Theory and Applications of Fractional Differential Equations
TL;DR: In this article, the authors present a method for solving Fractional Differential Equations (DFE) using Integral Transform Methods for Explicit Solutions to FractionAL Differentially Equations.
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Introductory functional analysis with applications
TL;DR: In this paper, the spectral theory of linear operators in normed spaces and their spectrum has been studied in the context of bounded self-and-adjoint linear operators and their applications in quantum mechanics.
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Long memory processes and fractional integration in econometrics
TL;DR: A survey and review of the major econometric work on long memory processes, fractional integration, and their applications in economics and finance and some of the definitions of long memory are reviewed.
Journal ArticleDOI
Approximate analytical solution for seepage flow with fractional derivatives in porous media
TL;DR: In this article, a variational iteration method is used to give approximate solutions of the problem of seepage flow in porous media with fractional derivatives, and the results show that the proposed iteration method, requiring no linearization or small perturbation is very effective and convenient.
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