Certain Analysis of Solution for the Nonlinear Two-Point Boundary Value Problem with Caputo Fractional Derivative

Murad, Shayma Adil

doi:10.1155/2022/1385355

Cited by 4 publications

(1 citation statement)

References 35 publications

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“…The challenge of studying the existence and uniqueness solution is the study of its stability. Ulam-Hyers stability (UHS) is the most important types of stability is used in this field ( see [4,10,17,27,28,44], [7,25], [19]) Su [43], studied the existence of solutions for a coupled system of fractional differential equations:…”

Section: Introductionmentioning

confidence: 99%

Caputo-hadamard Fractional Differential Equations: Integral Boundary Condition System

MURAD,

RAFEEQ,

IBRAHIM

et al. 2023

Preprint

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The solvability of a fractional differential equation depends on various factors such as the type of equation, the order of the fractional derivative, the domain and boundary conditions, and the properties of the solution sought. In this paper, The solution of a system of Caputo-Hadamard fractional differential equations (SCH) with integral boundary condition is investigated. The existence theorem of solutions is established by means of the Krasnoselskii and Schaefer’s fixed point theorem. Further, the uniqueness result is presented which is based on Banach’s contraction principle. Finally, the stability of the given system in Ulam-Hyers sense is applied. Examples are considered for the verification of theoretical works.

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Section: Introductionmentioning

confidence: 99%

Caputo-hadamard Fractional Differential Equations: Integral Boundary Condition System

MURAD,

RAFEEQ,

IBRAHIM

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

Existence and Stability Results for Impulsive Implicit Fractional Differential Equations with Delay and Riesz–Caputo Derivative

et al. 2023

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Caputo-Hadamard fractional boundary-value problems in $ {\mathfrak{L}}^\mathfrak{p} $-spaces

Murad,

Rafeeq,

Abdeljawad

2024

MATH

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<abstract><p>The focal point of this investigation is the exploration of solutions for Caputo-Hadamard fractional differential equations with boundary conditions, and it follows the initial formulation of a model that is intended to address practical problems. The research emphasizes resolving the challenges associated with determining precise solutions across diverse scenarios. The application of the Burton-Kirk fixed-point theorem and the Kolmogorov compactness criterion in $ {\mathfrak{L}}^\mathfrak{p} $-spaces ensures the existence of the solution to our problem. Banach's theory is crucial for the establishment of solution uniqueness, and it is complemented by utilizing the Hölder inequality in integral analysis. Stability analyses from the Ulam-Hyers perspective provide key insights into the system's reliability. We have included practical examples, tables, and figures, thereby furnishing a comprehensive and multifaceted examination of the outcomes.</p></abstract>

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Certain Analysis of Solution for the Nonlinear Two-Point Boundary Value Problem with Caputo Fractional Derivative

Cited by 4 publications

References 35 publications

Caputo-hadamard Fractional Differential Equations: Integral Boundary Condition System

Caputo-hadamard Fractional Differential Equations: Integral Boundary Condition System

Existence and Stability Results for Impulsive Implicit Fractional Differential Equations with Delay and Riesz–Caputo Derivative

Caputo-Hadamard fractional boundary-value problems in $ {\mathfrak{L}}^\mathfrak{p} $-spaces

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