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A New Approach for the Solution of the Generalized Abel Integral Equation

Part of the Nonlinear Systems and Complexity book series (NSCH,volume 31)

Abstract

The famous tautochrone problem is solved firstly by Abel in 1820s. Although the fractional calculus is known with the name of Caputo since his valuable contributions to the theory, the findings of Abel through the solutions of this famous problem may be the first realization of the differentiation and integration of fractional order. Maybe the most well-known fractional type integral equation, the generalized Abel integral equation, was solved by Abel. In this study, an approximate solution of the generalized Abel integral equation is obtained via the generalized binomial theorem.

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Fig. 8.1

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Cosgun, T., Sari, M., Uslu, H. (2020). A New Approach for the Solution of the Generalized Abel Integral Equation. In: Machado, J., Özdemir, N., Baleanu, D. (eds) Numerical Solutions of Realistic Nonlinear Phenomena. Nonlinear Systems and Complexity, vol 31. Springer, Cham. https://doi.org/10.1007/978-3-030-37141-8_8

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