Mathematica Bohemica, Vol. 146, No. 3, pp. 363-374, 2021
Existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problems
Choukri Derbazi, Hadda Hammouche
Received January 12, 2019. Published online October 9, 2020.
Abstract: 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.
Keywords: fractional Langevin equation; Caputo fractional derivative; integrable solution; existence; uniqueness; initial value problem; fixed point theorem
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Affiliations: Choukri Derbazi, Hadda Hammouche, Department of Mathematics, Faculty of Sciences, University of Ghardaia, Scientific Zone, P.O. Box 455, Ghardaia 47000, Algeria, e-mail: choukriedp@yahoo.com, h.hammouche@yahoo.fr
