Using the iterative reproducing kernel method for solving a class of nonlinear fractional differential equations

DOI10.1080/00207160.2017.1284318zbMath1397.34027OpenAlexW2574159873MaRDI QIDQ3177478

Dan Tian, Shuhong Bao, Yu-Lan Wang, Zhi-yuan Li

Publication date: 25 July 2018

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

Full work available at URL: https://doi.org/10.1080/00207160.2017.1284318

zbMATH Keywords

boundary value problemsfractional differential equationsreproducing kernel Hilbert spaceTaylor formulasingular-coefficient

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Theoretical approximation of solutions to ordinary differential equations (34A45) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Fractional ordinary differential equations (34A08)

Related Items (2)

NUMERICAL SIMULATION OF THE FRACTIONAL-ORDER RÖSSLER CHAOTIC SYSTEMS WITH GRÜNWALD–LETNIKOV FRACTIONAL DERIVATIVE ⋮ Reproducing kernels: harmonic analysis and some of their applications

Cites Work

• Unnamed Item
• Unnamed Item
• A general form of the generalized Taylor's formula with some applications
• Editorial: Advances in fractional differential equations
• A new modification of the Adomian decomposition method for solving boundary value problems for higher order nonlinear differential equations
• The solution of a class of singularly perturbed two-point boundary value problems by the iterative reproducing kernel method
• Using reproducing kernel for solving a class of singularly perturbed problems
• A new method for solving singular fourth-order boundary value problems with mixed boundary conditions
• The Lie-group shooting method for solving the Bratu equation
• Approximate solution of the Fredholm integral equation of the first kind in a reproducing kernel Hilbert space
• Using reproducing kernel for solving a class of partial differential equation with variable-coefficients
• Variational iteration method for fifth-order boundary value problems using He's polynomials
• An efficient computational method for linear fifth-order two-point boundary value problems
• The numerical solution of fifth-order boundary value problems by the variational iteration method
• A numerical algorithm for solving a class of linear nonlocal boundary value problems
• Numerical comparison of methods for solving a special fourth-order boundary value problem
• New algorithm for second-order boundary value problems of integro-differential equation
• On positive solutions of a nonlocal fractional boundary value problem
• Numerical continuation and the Gelfand problem
• Cubic splines method for a system of third-order boundary value problems
• Reproducing kernel algorithm for the analytical-numerical solutions of nonlinear systems of singular periodic boundary value problems
• The numerical solution of fifth-order boundary value problems with sixth-degree B-spline functions
• Quartic splines solutions of third-order obstacle problems
• Error estimation for the reproducing kernel method to solve linear boundary value problems
• The modified decomposition method for eighth-order boundary value problems
• A new method for solving a class of singular two-point boundary value problems
• Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method
• A numerical algorithm for nonlinear multi-point boundary value problems
• Some error estimates for solving Volterra integral equations by using the reproducing kernel method
• The exact solution of system of linear operator equations in reproducing kernel spaces
• Nonpolynomial spline approach to the solution of a system of third-order boundary-value problems
• A COMPUTATIONAL METHOD FOR NONLINEAR 2M‐TH ORDER BOUNDARY VALUE PROBLEMS
• Solving nonlinear singular pseudoparabolic equations with nonlocal mixed conditions in the reproducing kernel space
• A REPRODUCING KERNEL METHOD FOR SOLVING A CLASS OF NONLINEAR SYSTEMS OF PDES
• B-spline method for solving Bratu's problem
• Solving the forced Duffing equation with integral boundary conditions in the reproducing kernel space
• Using reproducing kernel for solving a class of singular weakly nonlinear boundary value problems
• A reliable algorithm for solving boundary value problems for higher-order integro-differentiable equations
• The numerical solution of fifth-order boundary value problems by the decomposition method

This page was built for publication: Using the iterative reproducing kernel method for solving a class of nonlinear fractional differential equations