Multi-scale orthogonal basis method for nonlinear fractional equations with fractional integral boundary value conditions

DOI10.1016/j.amc.2020.125151OpenAlexW3014352518MaRDI QIDQ2177882

Wei Jiang, Zhaohong Yang, Ning Hu, Zhong Chen, Hai-Yang Song

Publication date: 7 May 2020

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2020.125151

zbMATH Keywords

Caputo derivativeNewton iteration method\(\varepsilon\)-approximate solutionfractional integral boundary value conditionsmulti-scale orthogonal basis

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Nonlocal and multipoint boundary value problems for ordinary differential equations (34B10) Fractional ordinary differential equations (34A08)

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Cites Work

• Unnamed Item
• A nonlocal multi-point multi-term fractional boundary value problem with Riemann-Liouville type integral boundary conditions involving two indices
• Numerical treatment for solving the perturbed fractional PDEs using hybrid techniques
• Fractional Sturm-Liouville eigen-problems: theory and numerical approximation
• A reproducing kernel method for solving nonlocal fractional boundary value problems
• Relaxation oscillations in spruce-budworm interactions
• On the fractional signals and systems
• Fractional relaxation-oscillation and fractional diffusion-wave phenomena.
• Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models
• Approximate solution of linear and nonlinear fractional differential equations under \(m\)-point local and nonlocal boundary conditions
• Existence results for fractional-order differential equations with nonlocal multi-point-strip conditions involving Caputo derivative
• A space-time spectral collocation method for the two-dimensional variable-order fractional percolation equations
• A new spectral method using nonstandard singular basis functions for time-fractional differential equations
• Multilevel augmentation methods for differential equations
• Existence and uniqueness of mild solutions for semilinear integro-differential equations of fractional order with nonlocal initial conditions and delays
• A class of time‐fractional reaction‐diffusion equation with nonlocal boundary condition
• The Finite Difference Methods for Fractional Ordinary Differential Equations
• Existence and uniqueness results for a class of fractional differential equations with an integral fractional boundary condition