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

Abstract

This paper presents the following AB-Caputo fractional boundary value problem (Equation Presented) with integral-type boundary conditions (Equation Presented) 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
DOIs	https://doi.org/10.1142/S0218348X24400413
Publication status	Published - 2024
Externally published	Yes

Keywords

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

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10.1142/S0218348X24400413

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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 (Equation Presented) with integral-type boundary conditions (Equation Presented) of order 2 < α ≤ 3. Schauder and Krasnoselskii{\textquoteright}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, Existence Results, Schauder Fixed Point Theorem, Stability, Uniqueness Krasnoselskii{\textquoteright}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} The Author(s)",

year = "2024",

doi = "10.1142/S0218348X24400413",

language = "English",

journal = "Fractals",

issn = "0218-348X",

publisher = "World Scientific Publishing Co. Pte Ltd",

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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: © The Author(s)

PY - 2024

Y1 - 2024

N2 - This paper presents the following AB-Caputo fractional boundary value problem (Equation Presented) with integral-type boundary conditions (Equation Presented) 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 (Equation Presented) with integral-type boundary conditions (Equation Presented) 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

KW - Existence Results

KW - Schauder Fixed Point Theorem

KW - Stability

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

JO - Fractals

JF - Fractals

M1 - 2440041

ER -

EXISTENCE AND STABILITY RESULTS OF FRACTIONAL DIFFERENTIAL EQUATIONS MITTAG-LEFFLER KERNEL

Abstract

Keywords

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