| Citation: |
H. Dehestani, Y. Ordokhani. IMPROVEMENT OF THE SPECTRAL METHOD FOR SOLVING MULTI-TERM TIME-SPACE RIESZ-CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2022, 12(6): 2600-2620. doi: 10.11948/20220146
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IMPROVEMENT OF THE SPECTRAL METHOD FOR SOLVING MULTI-TERM TIME-SPACE RIESZ-CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS
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Abstract
In this paper, we study the numerical solution of multi-term time-space Riesz-Caputo fractional differential equations with the help of shifted Vieta-Lucas polynomials. To get the desired purpose, we introduce a new method for obtaining the operational matrices. The constructed method for finding the matrices influence directly in the accuracy of the methodology. Thus, the combination of shifted Vieta-Lucas polynomials properties with the operational matrices has reduced the problem to a system of algebraic equations. The proposed approach provides the approximate solutions to the problem which are convergent to the exact solution. Finally, we represent the accuracy and efficiency of the methodology by examining some examples and presenting the results in the form of graphs and tables.
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References
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H. Dehestani, Y. Ordokhani. IMPROVEMENT OF THE SPECTRAL METHOD FOR SOLVING MULTI-TERM TIME-SPACE RIESZ-CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2022, 12(6): 2600-2620. doi: 10.11948/20220146
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Figure 1.
The absolute error for
$ M_{1}=3,M_{2}=2 $ $ \alpha=0.8 $ $ \beta=1.25 $ -
Figure 2.
The absolute error for
$ \beta=1.5 $ $ \beta=1.9 $ $ M_{1}=5,M_{2}=4 $ -
Figure 3.
The absolute error for
$ M_{2}=5 $ $ M_{2}=8 $ $ M_{1}=5, $ $ \beta=1.6 $ $ L=2 $ -
Figure 4.
Approximate solution for diverse values of
$ \alpha $ $ M_{2}=M_{1}=5, $ $ \beta=1.3 $ $ L=1 $ $ t=0.8 $ -
Figure 5.
Approximate solution at diverse times
$ t=0.1,0.3,0.5,0.7,0.9 $ $ M_{1}=M_{2}=5 $ $ \beta=1.9 $ -
Figure 6.
Error for
$ \alpha=0.75,\nu=0.35,\gamma=0.45,\beta=1.5 $ $ M_{1}=3,M_{2}=2 $ -
Figure 7.
The approximate solution (left) and the absolute error (right) for
$ \beta=1.3 $ $ M_{1}=3,M_{2}=8 $