Applications of Krasnoselskii-Dhage Type Fixed-Point Theorems to Fractional Hybrid Differential Equations

Akhadkulov, Habibulla; Alsharari, Fahad; Ying, Teh Yuan

doi:10.5556/j.tkjm.52.2021.3330

Cited by 3 publications

(2 citation statements)

References 19 publications

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“…The technique has been used to establish the existence and approximation of various kinds of differential equations, such as neutral functional differential equations with delay and maxima, quadratic fractional integral equations with maxima, and hybrid functional differential equations. For more results, see [8,20,21].…”

Section: Introductionmentioning

confidence: 99%

“…In [8], the authors discussed via a new version of Kransoselskii-type fixed-point theorem under a nonlinear D-contraction condition (see Dhage's version of Kransoselskii-type fixed-point theorem [15]) the following fractional hybrid differential equation involving the Riemann-Liouville differential and integral operators of orders 0 < λ < 1 and γ > 0:…”

Section: Introductionmentioning

confidence: 99%

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Lakshmikantham Monotone Iterative Principle for Hybrid Atangana-Baleanu-Caputo Fractional Differential Equations

Benkhettou

Salim

Lazreg

et al. 2023

Annals of West University of Timisoara - Mathematics and Computer Science

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In this paper, we study the following fractional differential equation involving the Atangana-Baleanu-Caputo fractional derivative: { A B C a D τ θ [ x ( ϑ ) − F ( ϑ , x ( ϑ ) ) ] = G ( ϑ , x ( ϑ ) ) , ϑ ∈ J : = [ a , b ] , x ( a ) = φ a ∈ ℝ . $$\left\{ {\matrix{ {AB{C_a}D_\tau ^\theta [x(\vartheta ) - F(\vartheta ,x(\vartheta ))] = G(\vartheta ,x(\vartheta )),\;\;\;{\kern 1pt} \vartheta \in J: = [a,b],} \hfill \cr {x(a) = {\varphi _a} \in .} \hfill \cr } } \right.$$ The result is based on a Dhage fixed point theorem. Further, an example is provided for the justification of our main result.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Lakshmikantham Monotone Iterative Principle for Hybrid Atangana-Baleanu-Caputo Fractional Differential Equations

Benkhettou

Salim

Lazreg

et al. 2023

Annals of West University of Timisoara - Mathematics and Computer Science

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On the solutions of fractional hybrid differential equations

Akhadkulov,

Eshkuvatov,

Roslan

et al. 2023

The 15th Universiti Malaysia Terengganu Annual Symposium 2021 (Umtas 2021)

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Analysis of a hybrid fractional coupled system of differential equations in $ n $-dimensional space with linear perturbation and nonlinear boundary conditions

Noor,

Ullah,

Ali

et al. 2024

MATH

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<abstract><p>In this paper, we investigated $ n $-dimensional fractional hybrid differential equations (FHDEs) with nonlinear boundary conditions in a nonlinear coupled system. For this purpose, we used Dhage's fixed point theory, and applied the Krasnoselskii-type coupled fixed point theorem to construct existence conditions of the solution of the FHDEs. To illustrated this idea, suitable examples are presented in $ 3 $-dimensional space at the end of the paper.</p></abstract>

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Applications of Krasnoselskii-Dhage Type Fixed-Point Theorems to Fractional Hybrid Differential Equations

Cited by 3 publications

References 19 publications

Lakshmikantham Monotone Iterative Principle for Hybrid Atangana-Baleanu-Caputo Fractional Differential Equations

Lakshmikantham Monotone Iterative Principle for Hybrid Atangana-Baleanu-Caputo Fractional Differential Equations

On the solutions of fractional hybrid differential equations

Analysis of a hybrid fractional coupled system of differential equations in $ n $-dimensional space with linear perturbation and nonlinear boundary conditions

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