Geodesic
Nonlinear Langevin time-delay differential equations with generalized Caputo fractional derivatives
Filomat, Tome 37 (2023) no. 19, p. 6487

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DOI

In a Banach space, we consider the nonlinear Langevin time-delay differential equations with ψ-Caputo fractional derivatives. Using weighted norms involving Mittag-Leffler functions, we obtain some existence and uniqueness of solutions of the problem. Besides, in some cases, the condition for the problem having a unique solution can be relaxed using Burton's method. We also obtain some Ulam-Hyers and Ulam-Hyers-Rassias Mittag-Leffler stability results for the main equation. Two examples are given to illustrate our theoretical findings.
DOI : 10.2298/FIL2319487D
Classification : 34A08, 26A33, 34A12
Keywords: Langevin time-delay equations, Generalized fractional Caputo derivative, Ulam-Hyers stability, Ulam-Hyers-Rassias stability, Mittag-Leffler functions 
Nguyen Minh Dien. Nonlinear Langevin time-delay differential equations with generalized Caputo fractional derivatives. Filomat, Tome 37 (2023) no. 19, p. 6487 . doi: 10.2298/FIL2319487D
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     author = {Nguyen Minh Dien},
     title = {Nonlinear {Langevin} time-delay differential equations with generalized {Caputo} fractional derivatives},
     journal = {Filomat},
     pages = {6487 },
     year = {2023},
     volume = {37},
     number = {19},
     doi = {10.2298/FIL2319487D},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2319487D/}
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