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چکیده
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The main idea of this paper is to establish the novel Hahn wavelets for solving fractional-order integro-differential equations (FIDEs). First, we introduce Hahn wavelets and some of their properties. Then, we convert FIDEs into integer-order integro-differential equations (IIDEs) using the Laplace transform method. Finally, the yielded IIDEs using the Hahn wavelets, activation functions, the Legendre–Gauss quadrature formula and collocation method transformed to a system of algebraic equations which can be easily solved by applying Newton’s iterative scheme. The computational approach has many advantages. One of the most important is to obtain the continuous and differentiable solution for FIDEs without using the operational matrix. Also, the convergence analysis is discussed in detail. At last, several numerical experiments are employed to clarify the performance and efficiency of the suggested method.
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