Geodesic
Hyers-Ulam stability of fractional integro-differential equation with a positive constant coefficient involving the generalized Caputo fractional derivative
Filomat, Tome 36 (2022) no. 18, p. 6299

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DOI

The purpose of this paper is to investigate the existence and uniqueness of a solution, and the continuous dependence on the input data of the solution of integro-differential equations with a positive constant coefficient involving fractional order derivative (FIDEs). In addition, we also provide the sufficient conditions for the Hyers-Ulam stability (HU-stability) and the Hyers-Ulam-Rassias stability (HUR-stability) of FIDEs. Finally, the HUR-stability of the well-known model of RLC circuit in the form of FIDEs is also surveyed.
DOI : 10.2298/FIL2218299V
Classification : 26A33, 34G20, 34A08, 34A12
Keywords: Fractional differential equations, Fractional integro–differential equations, Fixed point theorem, Gronwall’s inequality, Pachpatte’s inequality, Ulam stability, ψ−Caputo derivative 
Ho Vu; Ngo Van Hoa. Hyers-Ulam stability of fractional integro-differential equation with a positive constant coefficient involving the generalized Caputo fractional derivative. Filomat, Tome 36 (2022) no. 18, p. 6299 . doi: 10.2298/FIL2218299V
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     author = {Ho Vu and Ngo Van Hoa},
     title = {Hyers-Ulam stability of fractional integro-differential equation with a positive constant coefficient involving the generalized {Caputo} fractional derivative},
     journal = {Filomat},
     pages = {6299 },
     year = {2022},
     volume = {36},
     number = {18},
     doi = {10.2298/FIL2218299V},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2218299V/}
}
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