Existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problems

Choukri Derbazi; Hadda Hammouche

Mathematica Bohemica (2021)

  • Volume: 146, Issue: 3, page 363-374
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Derbazi, Choukri, and Hammouche, Hadda. "Existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problems." Mathematica Bohemica 146.3 (2021): 363-374. <http://eudml.org/doc/297535>.

@article{Derbazi2021,
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.},
author = {Derbazi, Choukri, Hammouche, Hadda},
journal = {Mathematica Bohemica},
keywords = {fractional Langevin equation; Caputo fractional derivative; integrable solution; existence; uniqueness; initial value problem; fixed point theorem},
language = {eng},
number = {3},
pages = {363-374},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problems},
url = {http://eudml.org/doc/297535},
volume = {146},
year = {2021},
}

TY - JOUR
AU - Derbazi, Choukri
AU - Hammouche, Hadda
TI - Existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problems
JO - Mathematica Bohemica
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 146
IS - 3
SP - 363
EP - 374
AB - 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.
LA - eng
KW - fractional Langevin equation; Caputo fractional derivative; integrable solution; existence; uniqueness; initial value problem; fixed point theorem
UR - http://eudml.org/doc/297535
ER -

References

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