Solving a linear fractional equation with nonlocal boundary conditions based on multiscale orthonormal bases method in the reproducing kernel space
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Wei Jiang
,
Zhong Chen
,
Ning Hu
Abstract
In recent years, the study of fractional differential equations has become a hot spot. It is more difficult to solve fractional differential equations with nonlocal boundary conditions. In this article, we propose a multiscale orthonormal bases collocation method for linear fractional-order nonlocal boundary value problems. In algorithm construction, the solution is expanded by the multiscale orthonormal bases of a reproducing kernel space. The nonlocal boundary conditions are transformed into operator equations, which are involved in finding the collocation coefficients as constrain conditions. In theory, the convergent order and stability analysis of the proposed method are presented rigorously. Finally, numerical examples show the stability, accuracy and effectiveness of the method.
Funding source: The National Natural Science foundation of China
Award Identifier / Grant number: 11401139
Acknowledgements
The authors would like to express their thanks to the unknown referees for their careful reading, helpful comments and valuable suggestions.
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Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: The work was supported by the National Natural Science foundation of China (Grant No. 11401139).
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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© 2020 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Original Research Articles
- Dynamic behavior of a stochastic SIRS model with two viruses
- Optimization approach to the constrained regulation problem for linear continuous-time fractional-order systems
- Systematic formulation of a general numerical framework for solving the two-dimensional convection–diffusion–reaction system
- Positive periodic solution for inertial neural networks with time-varying delays
- Stability analysis of almost periodic solutions for discontinuous bidirectional associative memory (BAM) neural networks with discrete and distributed delays
- Analysis of (α, β)-order coupled implicit Caputo fractional differential equations using topological degree method
- A new approach to the bienergy and biangle of a moving particle lying in a surface of lorentzian space
- Noninstantaneous impulsive and nonlocal Hilfer fractional stochastic integrodifferential equations with fractional Brownian motion and Poisson jumps
- Stress wave propagation in different number of fissured rock mass based on nonlinear analysis
- Analytical predictor–corrector entry guidance for hypersonic gliding vehicles
- Solving a linear fractional equation with nonlocal boundary conditions based on multiscale orthonormal bases method in the reproducing kernel space
- Anthropogenic climate change on a non-linear arctic sea-ice model of fractional Duffing oscillator
- Abundant rogue wave solutions for the (2 + 1)-dimensional generalized Korteweg–de Vries equation
- Invariant solutions of fractional-order spatio-temporal partial differential equations
Artikel in diesem Heft
- Frontmatter
- Original Research Articles
- Dynamic behavior of a stochastic SIRS model with two viruses
- Optimization approach to the constrained regulation problem for linear continuous-time fractional-order systems
- Systematic formulation of a general numerical framework for solving the two-dimensional convection–diffusion–reaction system
- Positive periodic solution for inertial neural networks with time-varying delays
- Stability analysis of almost periodic solutions for discontinuous bidirectional associative memory (BAM) neural networks with discrete and distributed delays
- Analysis of (α, β)-order coupled implicit Caputo fractional differential equations using topological degree method
- A new approach to the bienergy and biangle of a moving particle lying in a surface of lorentzian space
- Noninstantaneous impulsive and nonlocal Hilfer fractional stochastic integrodifferential equations with fractional Brownian motion and Poisson jumps
- Stress wave propagation in different number of fissured rock mass based on nonlinear analysis
- Analytical predictor–corrector entry guidance for hypersonic gliding vehicles
- Solving a linear fractional equation with nonlocal boundary conditions based on multiscale orthonormal bases method in the reproducing kernel space
- Anthropogenic climate change on a non-linear arctic sea-ice model of fractional Duffing oscillator
- Abundant rogue wave solutions for the (2 + 1)-dimensional generalized Korteweg–de Vries equation
- Invariant solutions of fractional-order spatio-temporal partial differential equations
