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Proper inverse operators of fractional derivatives with nonsingular kernels

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Abstract

In this paper, we present the proper fractional integral operators of the Atangana-Baleanu and Caputo-Fabrizio fractional derivatives of arbitrary order \(\alpha > 0.\) Unlike the previous integral operators, the new ones act as proper inverse operators of the Atangana-Baleanu and Caputo-Fabrizio derivatives. The higher order integral operators of the Atangana-Baleanu derivative are defined for the first time in the current work.

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  1. Department of Mathematics, Yarmouk University, Irbid, Jordan

    Mohammed Al-Refai

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  1. Mohammed Al-Refai
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Correspondence to Mohammed Al-Refai.

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Al-Refai, M. Proper inverse operators of fractional derivatives with nonsingular kernels. Rend. Circ. Mat. Palermo, II. Ser 71, 525–535 (2022). https://doi.org/10.1007/s12215-021-00638-2

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  • DOI: https://doi.org/10.1007/s12215-021-00638-2

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