A New Collocation Method for Solving Fractional Integro-di Erential Equations with the Weakly Singular Kernel Based on the Fractional Cα Space

Haizhen Zhang

Abstract


In this paper, a new collocation method based on fractional polynomials is proposed for solving fractional integro-di erential equations with weakly singular kernel. For solving the equation, the di culties lie in choosing the space of the exact solution. In this paper, we solve this problem perfectly and propose the concept of the fractional Cα space. Meanwhile, a dense subset of this fractional Cα space is obtained. Based on the fractional Cα space, a strict theory for obtaining the ε-approximate solution is established. Using our method, a small amount of calculation can gain an accuracy satisfying the application requirements. The e ciency of the proposed method is verified by the final numerical experiments through comparing with those reported in A fast numerical algorithm based on the second kind Chebyshev polynomials for fractional integro-di erential equations with weakly singular kernels.

Keywords


Collocation method; Fractional integro-di erential equations; Weakly singular kernel; Fractional Cα space

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References


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DOI: https://doi.org/10.36012/fhe.v3i1.3361

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