Existence and Uniqueness of Mild Solution for Fractional-Order Controlled Fuzzy Evolution Equation

Iqbal, Naveed; Niazi, Azmat Ullah Khan; Shafqat, Ramsha; Zaland, Shamsullah

doi:10.1155/2021/5795065

Cited by 23 publications

(14 citation statements)

References 24 publications

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“…For k = 2, let us employ Caputo fractional differential operator C gH D α 2 to both sides of the first equation in (22). Then, from (20), one can get…”

Section: Remarkmentioning

confidence: 99%

“…In 2021, Niazi and Iqbal studied a class of Caputo fuzzy fractional evolution equations and obtained some important conclusions such as precise controllability of the evolution equations and existence and uniqueness of mild solutions (see [19][20][21]). About 10 years ago, Agarwal et al [22] and Arshad and Lupulescu [23] applied different methods to prove the existence and uniqueness of solutions for fuzzy fractional ordinary differential equations.…”

Section: Introductionmentioning

confidence: 99%

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Initial Value Problems of Fuzzy Fractional Coupled Partial Differential Equations with Caputo gH-Type Derivatives

Zhang

Lan

2022

Fractal Fract

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The purpose of this paper is to investigate a class of initial value problems of fuzzy fractional coupled partial differential equations with Caputo gH-type derivatives. Firstly, using Banach fixed point theorem and the mathematical inductive method, we prove the existence and uniqueness of two kinds of gH-weak solutions of the coupled system for fuzzy fractional partial differential equations under Lipschitz conditions. Then we give an example to illustrate the correctness of the existence and uniqueness results. Furthermore, because of the coupling in the initial value problems, we develop Gronwall inequality of the vector form, and creatively discuss continuous dependence of the solutions of the coupled system for fuzzy fractional partial differential equations on the initial values and ε-approximate solution of the coupled system. Finally, we propose some work for future research.

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“…For k = 2, let us employ Caputo fractional differential operator C gH D α 2 to both sides of the first equation in (22). Then, from (20), one can get…”

Section: Remarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Initial Value Problems of Fuzzy Fractional Coupled Partial Differential Equations with Caputo gH-Type Derivatives

Zhang

Lan

2022

Fractal Fract

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“…Some researchers examined the stability of fuzzy DEs [33]. Niazi et al [34], Iqbal et al [35], Shafqat et al [36] and Abuasbeh et al [37] investigated the existence and uniqueness of the FFEE. Ahmad et al [38] worked on Model (2), the fuzzy fractional-order model of the novel coronavirus as…”

Section: Introductionmentioning

confidence: 99%

Pattern Formation Induced by Fuzzy Fractional-Order Model of COVID-19

Alnahdi

Shafqat

Niazi

et al. 2022

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A novel coronavirus infection system is established for the analytical and computational aspects of this study, using a fuzzy fractional evolution equation (FFEE) stated in Caputo’s sense for order (1,2). It is constructed using the FFEE formulated in Caputo’s meaning. The model consist of six components illustrating the coronavirus outbreak, involving the susceptible people Kℓ(ω), the exposed population Lℓ(ω), total infected strength Cℓ(ω), asymptotically infected population Mℓ(ω), total number of humans recovered Eℓ(ω), and reservoir Qℓ(ω). Numerical results using the fuzzy Laplace approach in combination with the Adomian decomposition transform are developed to better understand the dynamical structures of the physical behavior of COVID-19. For the controlling model, such behavior on the generic characteristics of RNA in COVID-19 is also examined. The findings show that the proposed technique of addressing the uncertainty issue in a pandemic situation is effective.

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“…Abbas et al [21,22] worked on a partial differential equation. Niazi et al [23,24], Iqbal et al [25], Shafqat et al [26], Abuasbeh et al [27], and Alnahdi [28] existence-uniqueness of the FFEE were investigated. Arjunan et al [29][30][31][32] worked on the fractional differential inclusions.…”

Section: Introductionmentioning

confidence: 99%

Existence Results of Fuzzy Delay Impulsive Fractional Differential Equation by Fixed Point Theory Approach

Khan

Shafqat

Niazi

2022

Journal of Function Spaces

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The main aim of this article is to study controllability and existence of solution of fuzzy delay impulsive fractional nonlocal integro-differential equation in the sense of Caputo operator. The existence and uniqueness of the solution have been carried out with the help of the Banach fixed point theorem. Moreover, for fuzzy fractional differential equations (FFDEs) driven by the Liu process, this present work introduced a concept of stability in credibility space. Finally, efficient examples are presented to demonstrate the main theoretical findings.

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Existence and Uniqueness of Mild Solution for Fractional-Order Controlled Fuzzy Evolution Equation

Abstract: In this article, we investigated the existence and uniqueness of mild solutions for fractional-order controlled fuzzy evolution equations with Caputo derivatives of the controlled fuzzy nonlinear evolution equation of the form 0 c … Show more

Cited by 23 publications

References 24 publications

Initial Value Problems of Fuzzy Fractional Coupled Partial Differential Equations with Caputo gH-Type Derivatives

Initial Value Problems of Fuzzy Fractional Coupled Partial Differential Equations with Caputo gH-Type Derivatives

Pattern Formation Induced by Fuzzy Fractional-Order Model of COVID-19

Existence Results of Fuzzy Delay Impulsive Fractional Differential Equation by Fixed Point Theory Approach

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