TY - JOUR
T1 - Existence And Stability Results Of Fractional Differential Equations Mittag-Leffler Kernel
AU - Abbas, Ahsan
AU - Mehmood, Nayyar
AU - Akgül, Ali
AU - Amacha, Inas
AU - Abdeljawad, Thabet
N1 - Publisher Copyright:
© 2024 The Author(s).
PY - 2024
Y1 - 2024
N2 - This paper presents the following AB-Caputo fractional boundary value problem 0ABCDαu(ς) = (ς,u(ς)),ς [0, 1] with integral-type boundary conditions u(0) = 0 = u″(0),γu(1) = λ∫01g 1(ϰ)u(ϰ)dϰ, of order 2 < α ≤ 3. Schauder and Krasnoselskii's fixed point theorems are used to find existence results. Uniqueness is obtained via the Banach contraction principle. To investigate the stability of a given problem, Hyers-Ulam stability is discussed. An example is provided to validate our results.
AB - This paper presents the following AB-Caputo fractional boundary value problem 0ABCDαu(ς) = (ς,u(ς)),ς [0, 1] with integral-type boundary conditions u(0) = 0 = u″(0),γu(1) = λ∫01g 1(ϰ)u(ϰ)dϰ, of order 2 < α ≤ 3. Schauder and Krasnoselskii's fixed point theorems are used to find existence results. Uniqueness is obtained via the Banach contraction principle. To investigate the stability of a given problem, Hyers-Ulam stability is discussed. An example is provided to validate our results.
KW - AB-Caputo Fractional BVP
KW - Banach Contraction Principle and Stability
KW - Existence Results
KW - Schauder Fixed Point Theorem
KW - Uniqueness Krasnoselskii's Fixed Point Theorem
UR - http://www.scopus.com/inward/record.url?scp=85196944114&partnerID=8YFLogxK
U2 - 10.1142/S0218348X24400413
DO - 10.1142/S0218348X24400413
M3 - Article
AN - SCOPUS:85196944114
SN - 0218-348X
VL - 32
JO - Fractals
JF - Fractals
IS - 7-8
M1 - 2440041
ER -