Existence And Stability Results Of Fractional Differential Equations Mittag-Leffler Kernel

Ahsan Abbas; Nayyar Mehmood; Ali Akgül; Inas Amacha; Thabet Abdeljawad

doi:10.1142/S0218348X24400413

Existence And Stability Results Of Fractional Differential Equations Mittag-Leffler Kernel

Ahsan Abbas
, Nayyar Mehmood
, Ali Akgül
, Inas Amacha^*
, Thabet Abdeljawad

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

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.

Original language	English
Article number	2440041
Journal	Fractals
Volume	32
Issue number	7-8
DOIs	https://doi.org/10.1142/S0218348X24400413
Publication status	Published - 2024
Externally published	Yes

Keywords

AB-Caputo Fractional BVP
Banach Contraction Principle and Stability
Existence Results
Schauder Fixed Point Theorem
Uniqueness Krasnoselskii's Fixed Point Theorem

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Cite this

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title = "Existence And Stability Results Of Fractional Differential Equations Mittag-Leffler Kernel",

abstract = "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.",

keywords = "AB-Caputo Fractional BVP, Banach Contraction Principle and Stability, Existence Results, Schauder Fixed Point Theorem, Uniqueness Krasnoselskii's Fixed Point Theorem",

author = "Ahsan Abbas and Nayyar Mehmood and Ali Akg{\"u}l and Inas Amacha and Thabet Abdeljawad",

note = "Publisher Copyright: {\textcopyright} 2024 The Author(s).",

year = "2024",

doi = "10.1142/S0218348X24400413",

language = "English",

volume = "32",

journal = "Fractals",

issn = "0218-348X",

publisher = "World Scientific",

number = "7-8",

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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

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 - https://www.scopus.com/pages/publications/85196944114

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 -

Existence And Stability Results Of Fractional Differential Equations Mittag-Leffler Kernel

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