Geodesic
Existence and UH-stability of integral boundary problem for a class of nonlinear higher-order Hadamard fractional Langevin equation via Mittag-Leffler functions
Filomat, Tome 37 (2023) no. 4, p. 1053

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The Langevin equation is a very important mathematical model in describing the random motion of particles. The fractional Langevin equation is a powerful tool in complex viscoelasticity. Therefore, this paper focuses on a class of nonlinear higher-order Hadamard fractional Langevin equation with integral boundary value conditions. Firstly, we employ successive approximation and Mittag-Leffler function to transform the differential equation into an equivalent integral equation. Then the existence and uniqueness of the solution are obtained by using the fixed point theory. Meanwhile, the Ulam-Hyers (UH) stability is proved by inequality technique and direct analysis.
DOI : 10.2298/FIL2304053Z
Classification : 34B15, 34D20, 34K37
Keywords: UH-stability, Hadamard fractional Langevin equation, higher-order integral boundary problem, Mittag-Leffler function 
Kaihong Zhao. Existence and UH-stability of integral boundary problem for a class of nonlinear higher-order Hadamard fractional Langevin equation via Mittag-Leffler functions. Filomat, Tome 37 (2023) no. 4, p. 1053 . doi: 10.2298/FIL2304053Z
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     author = {Kaihong Zhao},
     title = {Existence and {UH-stability} of integral boundary problem for a class of nonlinear higher-order {Hadamard} fractional {Langevin} equation via {Mittag-Leffler} functions},
     journal = {Filomat},
     pages = {1053 },
     year = {2023},
     volume = {37},
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     doi = {10.2298/FIL2304053Z},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2304053Z/}
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