Ulam-Hyers stabilities of fractional functional differential equations

J. Vanterler da C. Sousa; E. Capelas de Oliveira; F. G. Rodrigues; J. Vanterler da C. Sousa; E. Capelas de Oliveira; F. G. Rodrigues

doi:10.3934/math.2020092

AIMS Mathematics

2020, Volume 5, Issue 2: 1346-1358. doi: 10.3934/math.2020092

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Research article

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

Received: 12 October 2019 Accepted: 17 January 2020 Published: 20 January 2020
MSC : 26A33, 34A08, 34K37, 34K20

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

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Abstract

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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