| Citation: |
Rohul Amin, Raheem Ullah, Imran Khan, Wojciech Sumelka. HAAR WAVELET METHOD WITH CAPUTO DERIVATIVE FOR SOLUTION OF A SYSTEM OF FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2025, 15(3): 1641-1658. doi: 10.11948/20240325
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HAAR WAVELET METHOD WITH CAPUTO DERIVATIVE FOR SOLUTION OF A SYSTEM OF FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS
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Abstract
In this paper, a numerical method based on Haar wavelet with Caputo derivative is developed for the solution of a system of fractional integro-differential equations (FIDEs). The solution of these equations is difficult due to the non-local nature of fractional derivatives and integrals. Different numerical and analytical methods have been developed to overcome these challenges. We develop numerical scheme for solution of different types of systems of FIDEs. The proposed method is then applied to different test problems to demonstrate its robustness and effectiveness. The experiential error analysis is carried out for all test problems. These experiments involve the calculation and analysis of different error norms, such as the maximum absolute error and root mean square error. The numerical experiment shows that increasing the collocation points the errors reduces significantly. The results show that the present numerical scheme is a precise and efficient technique for solving such systems of FIDEs.
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References
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Rohul Amin, Raheem Ullah, Imran Khan, Wojciech Sumelka. HAAR WAVELET METHOD WITH CAPUTO DERIVATIVE FOR SOLUTION OF A SYSTEM OF FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2025, 15(3): 1641-1658. doi: 10.11948/20240325
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Figure 1.
A comparative analysis of
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Figure 2.
A comparative analysis of
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Figure 3.
A comparative analysis of
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Figure 4.
A comparative analysis of
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Figure 5.
A comparative analysis of
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Figure 6.
A comparative analysis of
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