A Novel Implementation of Mönch’s Fixed Point Theorem to a System of Nonlinear Hadamard Fractional Differential Equations

Elaiw, Abeer Al; Awadalla, Muath; Manigandan, Murugesan; Abuasbeh, Kinda

doi:10.3390/fractalfract6100586

Cited by 8 publications

(3 citation statements)

References 33 publications

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“…Next, to exam the values p 1 (t), p 2 (t) and p 3 (t) for θ 1 (t) = ln(t) and θ 2 (t) = (ln(t)) 2 , from the Equation ( 27), we obtain ϵ 1 = 0.75 and ϵ 2 = 0.0731058. The behavior of p 1 (t), p 2 (t), and p 3 (t) can be see in the Figures (3,4). Then by Theorem(3.5), the problem(34) is Ulam-Hyers stable.…”

Section: Examplesmentioning

confidence: 86%

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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: Examplesmentioning

confidence: 86%

“…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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show abstract

“…For more information about, these scientifc papers, the reader can see [24][25][26][27][28][29][30][31], and the stability of solutions was studied after the existence of them. To enrich the reader, it is possible to see [32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Applicability of Darbo’s Fixed Point Theorem on the Existence of a Solution to Fractional Differential Equations of Sequential Type

Awadalla

Abuasbeh

Manigandan

et al. 2023

Journal of Mathematics

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In this article, we study the existence of the solution for the fractional differential equations of sequential type with nonlocal integral boundary conditions. The main results are established with the aid of Darbo’s fixed point theorem and Hausdorff’s measure of noncompactness method. The stability of the proposed fractional differential equation is also investigated via the Ulam–Hyer technique. In addition, an applied example that supports the theoretical results reached through this study is included.

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Stability and Uniqueness Results for the Nonseparated Boundary Conditions of Nonlinear Coupled System of Fractional Differential Equations

Al-khateeb,

Zureigat,

Batiha

et al. 2024

International Journal of Mathematics and Mathematical Sciences

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In this article, the focus is on investigating the uniqueness, existence, and stability of a coupled system of fractional differential equations with non‐separated coupled boundary conditions. The uniqueness of solutions for the presented problem is discussed by employing the fixed‐point theorem. The Leray–Schauder’s alternative is used to investigate the existence of solutions for the presented equation. A formulation of certain conditions for the Hyers–Ulam type stability of solutions pertaining to the boundary value problem (BVP) is discussed. Finally, two numerical examples are presented to examine and illustrate our results.

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A Novel Implementation of Mönch’s Fixed Point Theorem to a System of Nonlinear Hadamard Fractional Differential Equations

Cited by 8 publications

References 33 publications

Caputo-hadamard Fractional Differential Equations: Integral Boundary Condition System

Caputo-hadamard Fractional Differential Equations: Integral Boundary Condition System

Applicability of Darbo’s Fixed Point Theorem on the Existence of a Solution to Fractional Differential Equations of Sequential Type

Stability and Uniqueness Results for the Nonseparated Boundary Conditions of Nonlinear Coupled System of Fractional Differential Equations

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