Geodesic
Existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problems
Mathematica Bohemica, Tome 146 (2021) no. 3, pp. 363-374

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We study the existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problems. Our results are based on Schauder's fixed point theorem and the Banach contraction principle fixed point theorem. Examples are provided to illustrate the main results.
DOI : 10.21136/MB.2020.0004-19
Classification : 26A33, 34A08
Keywords: fractional Langevin equation; Caputo fractional derivative; integrable solution; existence; uniqueness; initial value problem; fixed point theorem 
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Derbazi, Choukri; Hammouche, Hadda. Existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problems. Mathematica Bohemica, Tome 146 (2021) no. 3, pp. 363-374. doi: 10.21136/MB.2020.0004-19

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