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Existence and approximate solutions for Hadamard fractional integral equations in a Banach space. (English) Zbl 1529.45002

Summary: We examine a class of fractional-order Volterra functional integral equations, where the fractional integral is viewed in the Hadamard type. By using Petryshyn’s fixed point theorem for Banach spaces, we investigate the existence of solutions for fractional integral equations. Also, we introduce an iterative method using the sinc quadrature rule to find the approximate solutions of Hadamard fractional integral equations. Several examples are presented to support the theoretical and numerical results.

MSC:

45D05 Volterra integral equations
65R20 Numerical methods for integral equations
26A33 Fractional derivatives and integrals
47H08 Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc.
47H10 Fixed-point theorems
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References:

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