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Abstract
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In the current article, our aim is to approach the answer of fractional integral-differential equations of variable order utilizing the generl fractional-order Fibonacci wavelets. Fractional-order Fibonacci wavelets and integral and derivative operational matrices are considered to be utilized. First of all, new integration and derivative functional matrices are obtained. Next, these matrices which are more accurate in analogy to the other functional matrices are used to alter the proposed equation by an algebraic system. Collocation method is utilized to resolve the obtained algebraic equations system to achieve the unfamiliar coefficients. At the end, error estimate and a number of examples are provided to assess the accuracy, validity, and effectiveness of the manner. Compared to other methods, this method has less error. We also analysis the convergence and the error bound of the present approach utilizing related theorems.
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