Numerical solution of fractional pantograph differential equations by using generalized fractional-order Bernoulli wavelet
TLDR
New functions based on the Bernoulli wavelets are defined to obtain the numerical solution of fractional-order pantograph differential equations in a large interval to reduce the problem to a set of algebraic equations.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2017-01-01 and is currently open access. It has received 128 citations till now. The article focuses on the topics: Fractional calculus & Bernoulli differential equation.read more
Citations
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Journal ArticleDOI
An efficient approximate method for solving delay fractional optimal control problems
TL;DR: In this paper, a new numerical method for solving the delay fractional optimal control problems (DFOCPs) with quadratic performance index is presented, which is based upon the Bernoulli wavelets basis.
Journal ArticleDOI
Fractional-order Legendre–Laguerre functions and their applications in fractional partial differential equations
TL;DR: This paper considers a new fractional function based on Legendre and Laguerre polynomials for solving a class of linear and nonlinear time-space fractional partial differential equations with variable coefficients and calculates the upper bound for the error of integral operational matrix of the fractional order.
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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Journal ArticleDOI
Fast wavelet transforms and numerical algorithms I
TL;DR: The algorithms presented here are based on the recently developed theory of wavelets and are applicable to all Calderon-Zygmund and pseudo-differential operators, and indicate that many previously intractable problems become manageable with the techniques presented here.
Posted Content
Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics
TL;DR: In this article, the authors review some applications of fractional calculus developed by the author (partly in collaboration with others) to treat some basic problems in continuum and statistical mechanics.
Journal ArticleDOI
Fractional calculus models of complex dynamics in biological tissues
TL;DR: Three areas of bioengineering research (bioelectrodes, biomechanics, bioimaging) are described where fractional calculus is being applied to build new mathematical models that predict macroscale behavior from microscale observations and measurements.
Journal ArticleDOI
A new operational matrix for solving fractional-order differential equations
Abbas Saadatmandi,Mehdi Dehghan +1 more
TL;DR: The main aim is to generalize the Legendre operational matrix to the fractional calculus and reduces such problems to those of solving a system of algebraic equations thus greatly simplifying the problem.
Journal ArticleDOI
Fractional calculus in the transient analysis of viscoelastically damped structures
Ronald L. Bagley,Peter J. Torvik +1 more
TL;DR: In this article, the authors used fractional calculus to model the viscoelastic behavior of a damping layer in a simply supported beam and analyzed the beam by using both a continuum formulation and a finite element formulation to predict the transient response to a step loading.
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