Open AccessEXISTENCE AND STABILITY ANALYSIS OF SOLUTIONS FOR FRACTIONAL LANGEVIN EQUATION WITH NONLOCAL INTEGRAL AND ANTI-PERIODIC-TYPE BOUNDARY CONDITIONS
Author(s) -
A. Durga Devi,
Anoop Kumar,
Thabet Abdeljawad,
Aziz Khan
Publication year - 2020
Publication title -
fractals
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.654
H-Index - 44
eISSN - 1793-6543
pISSN - 0218-348X
DOI - 10.1142/s0218348x2040006x
Subject(s) - mathematics , uniqueness , fixed point theorem , mathematical analysis , contraction principle , type (biology) , nonlinear system , fixed point , contraction mapping , banach fixed point theorem , stability (learning theory) , fractional calculus , boundary value problem , contraction (grammar) , physics , ecology , quantum mechanics , machine learning , medicine , computer science , biology
In this paper, we deal with the existence and uniqueness (EU) of solutions for nonlinear Langevin fractional differential equations (FDE) having fractional derivative of different orders with nonlocal integral and anti-periodic-type boundary conditions. Also, we investigate the Hyres–Ulam (HU) stability of solutions. The existence result is derived by applying Krasnoselskii’s fixed point theorem and the uniqueness of result is established by applying Banach contraction mapping principle. An example is offered to ensure the validity of our obtained results.