A New Reproducing Kernel Approach for Nonlinear Fractional Three-Point Boundary Value Problems
Abstract
:1. Introduction
2. Preliminaries
- (1)
- (2)
- .
3. Main Results
3.1. Generation of Reproducing Kernel for Three-Point Boundary Value Problems
3.2. Representation of Solution in Hilbert Space
3.3. Construction of Iterative Procedure
4. Numerical Applications
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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x | |||||
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0 | 0 | 0 | 0 | 0 | 0 |
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0.5 | 0 | 0 | 0 | 0 | 0 |
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0.9 | |||||
1 | 0 | 0 | 0 | 0 | 0 |
x | |||||
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0 | 0 | 0 | 0 | 0 | 0 |
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0.5 | 0 | 0 | 0 | 0 | 0 |
0.6 | |||||
0.7 | |||||
0.8 | |||||
0.9 | |||||
1 | 0 | 0 | 0 | 0 | 0 |
x | Exact Sol. | Approximate Sol. | Absolute Error |
---|---|---|---|
0.0 | 0.000000000000000000000 | 0.000000000000000000000 | 0 |
0.1 | 0.036000000000000000000 | 0.036000000000000000018 | |
0.2 | 0.048000000000000000000 | 0.048000000000000000044 | |
0.3 | 0.042000000000000000000 | 0.042000000000000000061 | |
0.4 | 0.024000000000000000000 | 0.024000000000000000071 | |
0.5 | 0.000000000000000000000 | 0.000000000000000000000 | 0 |
0.6 | |||
0.7 | |||
0.8 | |||
0.9 | |||
1 | 0 |
x | |||||
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0 | 0 | 0 | 0 | 0 | 0 |
0.1 | |||||
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0.3 | |||||
0.4 | |||||
0.5 | |||||
0.6 | 0 | 0 | 0 | 0 | 0 |
0.7 | |||||
0.8 | |||||
0.9 | |||||
1 | 0 | 0 | 0 | 0 | 0 |
x | |||||
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0 | 0 | 0 | 0 | 0 | 0 |
0.1 | |||||
0.2 | |||||
0.3 | |||||
0.4 | |||||
0.5 | |||||
0.6 | 0 | 0 | 0 | 0 | 0 |
0.7 | |||||
0.8 | |||||
0.9 | |||||
1 | 0 | 0 | 0 | 0 | 0 |
x | Exact Sol. | Approximate Sol. | Absolute Error |
---|---|---|---|
0.0 | 0.000000000000000000000 | 0.000000000000000000000 | 0 |
0.1 | 0.045000000000000000000 | 0.045000000000480782793 | |
0.2 | 0.064000000000000000000 | 0.064000000000580045412 | |
0.3 | 0.063000000000000000000 | 0.063000000000488602930 | |
0.4 | 0.048000000000000000000 | 0.048000000000398645450 | |
0.5 | 0.025000000000000000000 | 0.025000000000468872800 | |
0.6 | 0.000000000000000000000 | 0.000000000000000000000 | 0 |
0.7 | |||
0.8 | |||
0.9 | |||
1 | 0.000000000000000000000 | 0.000000000000000000000 | 0 |
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Sakar, M.G.; Saldır, O. A New Reproducing Kernel Approach for Nonlinear Fractional Three-Point Boundary Value Problems. Fractal Fract. 2020, 4, 53. https://doi.org/10.3390/fractalfract4040053
Sakar MG, Saldır O. A New Reproducing Kernel Approach for Nonlinear Fractional Three-Point Boundary Value Problems. Fractal and Fractional. 2020; 4(4):53. https://doi.org/10.3390/fractalfract4040053
Chicago/Turabian StyleSakar, Mehmet Giyas, and Onur Saldır. 2020. "A New Reproducing Kernel Approach for Nonlinear Fractional Three-Point Boundary Value Problems" Fractal and Fractional 4, no. 4: 53. https://doi.org/10.3390/fractalfract4040053
APA StyleSakar, M. G., & Saldır, O. (2020). A New Reproducing Kernel Approach for Nonlinear Fractional Three-Point Boundary Value Problems. Fractal and Fractional, 4(4), 53. https://doi.org/10.3390/fractalfract4040053