Numerical algorithm to solve generalized fractional pantograph equations with variable coefficients based on shifted Chebyshev polynomials

DOI10.1080/00207160.2019.1573992OpenAlexW2914021327WikidataQ128526498 ScholiaQ128526498MaRDI QIDQ5031762

Driss Boutat, Da-Yan Liu, Li-Ping Wang, Yi-Ming Chen

Publication date: 16 February 2022

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160.2019.1573992

zbMATH Keywords

error analysisnumerical solutionoperational matrixshifted Chebyshev polynomialsgeneralized fractional pantograph equations

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Numerical methods for initial value problems involving ordinary differential equations (65L05) Approximation by polynomials (41A10) Approximation by operators (in particular, by integral operators) (41A35) Functional-differential equations with fractional derivatives (34K37) Numerical analysis (65-XX)

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Cites Work

• Unnamed Item
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• Numerical solution of fractional partial differential equations with variable coefficients using generalized fractional-order Legendre functions
• Numerical solution of fractional pantograph differential equations by using generalized fractional-order Bernoulli wavelet
• A collocation method based on Bernoulli operational matrix for numerical solution of generalized pantograph equation
• A new operational matrix based on Bernoulli wavelets for solving fractional delay differential equations
• Galerkin finite element method for nonlinear fractional Schrödinger equations
• Non-asymptotic fractional order differentiator for a class of fractional order linear systems
• Variational iteration method for solving the multi -- pantograph delay equation
• A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order
• A new numerical technique for solving the local fractional diffusion equation: two-dimensional extended differential transform approach
• Numerical solution of nonlinear Volterra integro-differential equations of arbitrary order by CAS wavelets
• Second kind shifted Chebyshev polynomials for solving space fractional order diffusion equation
• Fractional relaxation-oscillation and fractional diffusion-wave phenomena.
• Fractional calculus models of complex dynamics in biological tissues
• A new operational matrix for solving fractional-order differential equations
• The variational iteration method for solving a neutral functional-differential equation with proportional delays
• On the one-leg \(\theta \)-methods for solving nonlinear neutral functional differential equations
• An effective numerical method for solving fractional pantograph differential equations using modification of hat functions
• Modified Chebyshev wavelet methods for fractional delay-type equations
• A fast linearized conservative finite element method for the strongly coupled nonlinear fractional Schrödinger equations
• Innovative fractional derivative estimation of the pseudo-state for a class of fractional order linear systems
• Numerical solutions for systems of fractional differential equations by the decomposition method
• Long memory processes and fractional integration in econometrics
• Numerical solution of the delay differential equations of pantograph type via Chebyshev polynomials
• The twisted Daehee numbers and polynomials
• Spectral-collocation methods for fractional pantograph delay-integrodifferential equations
• A fast energy conserving finite element method for the nonlinear fractional Schrödinger equation with wave operator
• An \(h\)-\(p\) version of the continuous Petrov-Galerkin finite element method for Riemann-Liouville fractional differential equation with novel test basis functions
• Analysis and numerical methods for fractional differential equations with delay
• Solving systems of fractional differential equations using differential transform method
• Fractional Order Differentiation by Integration and Error Analysis in Noisy Environment
• Numerical solution of system of first-order delay differential equations using polynomial spline functions
• A Taylor polynomial approach for solving generalized pantograph equations with nonhomogenous term
• A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity
• Analysis of a Model Representing Stage-Structured Population Growth with State-Dependent Time Delay
• The use of Jacobi polynomials in the numerical solution of coupled system of fractional differential equations
• Nonasymptotic Pseudo-State Estimation for a Class of Fractional Order Linear Systems
• Stability of the Discretized Pantograph Differential Equation
• NUMERICAL SOLUTION OF FRACTIONAL DELAY DIFFERENTIAL EQUATIONS USING SPLINE FUNCTIONS
• Discretized Stability and Error Growth of The Nonautonomous Pantograph Equation