ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 17 (2022), 225 -- 239
This work is licensed under a Creative Commons Attribution 4.0 International License.
EXISTENCE RESULTS FOR LANGEVIN EQUATION WITH RIESZ-CAPUTO FRACTIONAL DERIVATIVE
Naas Adjimi and Maamar Benbachir
Abstract. In this paper, we examine existence and uniqueness of solutions for nonlinear Langevin equation involving Riesz-Caputo fractional derivatives, with a class of anti-periodic boundary conditions. By applying a variety of fixed point theorems as Banach, Schaefer and Krasnoselskii fixed point theorems. Three examples are given to illustrate main results.
2020 Mathematics Subject Classification: 26A33, 34B25, 34B15
Keywords: Langevin equation; Riesz-Caputo derivative; fixed point theorems.
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Naas Adjimi
Laboratory of Mathematics and Applied Sciences University of Ghardaia, 47000, Algeria.
e-mail: naasadjimi@gmail.com
Maamar Benbachir
Faculty of Sciences, Saad Dahlab University, Blida, Algeria.
e-mail: mbenbachir2001@gmail.com