AIMS Mathematics, 2020, 5(2): 1346-1358. doi: 10.3934/math.2020092.

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Ulam-Hyers stabilities of fractional functional differential equations

1 Department of Applied Mathematics, Imecc-Unicamp, 13083-859, Campinas, SP, Brazil
2 Departamento de Matemáticas, Universidad de la Serena, Benavente 980, La Serena, Chile

From the first results on Ulam-Hyers stability, what has been noted is the exponential growth of the researchers dedicated to investigating Ulam-Hyers stability of fractional differential equation solutions whether they are functional, evolution, impulsive, among others. However, some issues and problems still need to be addressed. An intensifying problem is the small amount of work on Ulam-Hyers stability of solutions of fractional functional differential equations through more general fractional operators. In this sense, in this paper, we present a study on the Ulam-Hyers and UlamHyers-Rassias stabilities of the solution of the fractional functional differential equation using the Banach fixed point theorem.
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Keywords ψ-Hilfer fractional derivative; Ulam-Hyers stability; Ulam-Hyers-Rassias stability; fractional functional differential equations; Banach fixed point theorem

Citation: J. Vanterler da C. Sousa, E. Capelas de Oliveira, F. G. Rodrigues. Ulam-Hyers stabilities of fractional functional differential equations. AIMS Mathematics, 2020, 5(2): 1346-1358. doi: 10.3934/math.2020092


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