Open AccessMATHEMATICAL ANALYSIS OF COUPLED SYSTEMS WITH FRACTIONAL ORDER BOUNDARY CONDITIONS
Author(s) -
Zeeshan Ali,
Kamal Shah,
Akbar Zada,
Poom Kumam
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/s0218348x20400125
Subject(s) - mathematics , uniqueness , contraction principle , fixed point theorem , boundary value problem , generalization , ordinary differential equation , mathematical analysis , order (exchange) , fractional calculus , contraction mapping , stability (learning theory) , differential equation , finance , machine learning , computer science , economics
In this paper, we prove the existence, uniqueness and various kinds of Ulam stability for fractional order coupled systems with fractional order boundary conditions involving Riemann–Liouville fractional derivatives. The standard fixed point theorem like Leray–Schauder alternative and Banach contraction are applied to establish the existence theory and uniqueness. Furthermore, we build sufficient conditions for the stability mentioned above by two methods. Also, an example is given to illustrate our theoretical results. The proposed problem is the generalization of third-order ordinary differential equations with classical, initial and anti-periodic boundary conditions.