A reproducing kernel Hilbert space method for solving integro-differential equations of fractional order

DOI10.1007/s10957-012-0207-2zbMath1273.65194OpenAlexW2015597220MaRDI QIDQ1949559

Yong Zhou, Shaher Momani, Samia Bushnaq

Publication date: 8 May 2013

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10957-012-0207-2

zbMATH Keywords

algorithmiterative methodreproducing kernel Hilbert space methodnonlinear integro-differential equations of fractional order

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Numerical methods for integral equations (65R20) Other nonlinear integral equations (45G10) Fractional derivatives and integrals (26A33) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22)

Related Items (12)

Iterative reproducing kernel Hilbert spaces method for Riccati differential equations ⋮ High order algorithms for numerical solution of fractional differential equations ⋮ A fractional multiterm Gronwall lemma and its application to the stability of fractional integrodifferential systems ⋮ A new multiscale algorithm for solving second order boundary value problems ⋮ An efficient numerical algorithm for solving nonlinear fractional Volterra integro-differential equation ⋮ A modified reproducing Kernel Hilbert space method for solving fuzzy fractional integro-differential equations ⋮ Unnamed Item ⋮ A reproducing kernel Hilbert space method for solving systems of fractional integrodifferential equations ⋮ Solutions of nonlinear systems by reproducing kernel method ⋮ Iterative multistep reproducing kernel Hilbert space method for solving strongly nonlinear oscillators ⋮ Sensitivity of a fractional integrodifferential Cauchy problem of Volterra type ⋮ Application of a global implicit function theorem to a general fractional integro-differential system of Volterra type

Cites Work

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• Stability and non-standard finite difference method of the generalized Chua's circuit
• Homotopy analysis method for fractional IVPs
• Solving nonlinear pseudoparabolic equations with nonlocal boundary conditions in reproducing kernel space
• The exact solution of a linear integral equation with weakly singular kernel
• A novel method for nonlinear fractional partial differential equations: Combination of DTM and generalized Taylor's formula
• The homotopy analysis method for handling systems of fractional differential equations
• A reliable algorithm of homotopy analysis method for solving nonlinear fractional differential equations
• The variational iteration method: an efficient scheme for handling fractional partial differential equations in fluid mechanics
• Fractals and fractional calculus in continuum mechanics
• The exact solution for solving a class nonlinear operator equations in the reproducing kernel space.
• Analytical approximate solution for fractional heat-like and wave-like equations with variable coefficients using the decomposition method
• Detailed error analysis for a fractional Adams method
• Generalized differential transform method: Application to differential equations of fractional order
• Analytic and approximate solutions of the space- and time-fractional telegraph equations
• A COMPUTATIONAL METHOD FOR NONLINEAR 2M‐TH ORDER BOUNDARY VALUE PROBLEMS
• Variational iteration method for solving the space‐ and time‐fractional KdV equation
• Analysis of fractional differential equations

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