An extension of Krasnoselskii’s fixed point theorem and its application to nonlocal problems for implicit fractional differential systems with uncertainty

Long, Hoàng Việt; Dong, Nguyen Phuong

doi:10.1007/s11784-018-0507-8

Cited by 29 publications

(16 citation statements)

References 29 publications

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“…By using similar arguments as in Long and Dong (2018), we obtain that the space C, D gr ∞ is a complete metric space. Moreover, for simplicity, we denote J ∞ = [0, ∞) and C χ := C([−χ, 0], E) by the functional space endowed with the metric…”

Section: Definition 22 Mazandarani Et Al (2018)mentioning

confidence: 73%

Fuzzy delay differential equations under granular differentiability with applications

Son¹,

Long

Dong

2019

Comp. Appl. Math.

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In this paper, we consider a new setting of fuzzy delay differential equations by employing the concepts of granular differentiability. Firstly, we establish some basic properties of complete granular metric space. Then we study the local and global existence and uniqueness of integral fuzzy solution. For the first task, we use successive approximation technique combined with Gronwall's lemma. The second task will be solved by Banach contraction principle in weighted metric space defined by granular distance. Additionally, we demonstrate the theoretical results by solving some real-world models in both analytical method and numerical method. The first model is often referred to the exponential growth, namely time-delay growth Malthusian model. The second model is one type of dynamical systems, which is used for studies involving large amounts of tissues, called Ehrlich ascites tumor model with delay. Furthermore, we introduce the Mackey-Glass model which is considered as a useful tool for times series prediction in the neutral network and fuzzy logic fields. Finally, we represent the surface of fuzzy solution for visible identification mark-on. Keywords Granular differentiability • Fuzzy delay differential equations • Malthusian growth model • Ehrlich ascites tumor model • Mackey-Glass time series model Mathematics Subject Classification 34A07 • 35R13 Communicated by Anibal Tavares de Azevedo.

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Section: Definition 22 Mazandarani Et Al (2018)mentioning

confidence: 73%

Fuzzy delay differential equations under granular differentiability with applications

Son¹,

Long

Dong

2019

Comp. Appl. Math.

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“…We gave an example of the fractional dynamical system to illustrate the abstract fixed point proposed theorem. The results are interesting and can be directly applied to some other interesting problems such as the nonlocal problems for fuzzy implicit fractional differential systems [14] and fuzzyvalued equations [15].…”

Section: Discussionmentioning

confidence: 99%

Krasnoselskii N-Tupled Fixed Point Theorem with Applications to Fractional Nonlinear Dynamical System

Nabil

2019

Advances in Mathematical Physics

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In this paper, N-tupled fixed point theorems for two monotone nondecreasing mappings in complete normed linear space are established. The extension of Krasnoseskii fixed point theorem for a version of N-tupled fixed point is given. Our theoretical results are applied to prove the existence of a mild solution of the system of N-nonlinear fractional evolution equations. Finally, an example of a nonlinear fractional dynamical system is given to illustrate the results.

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“…Very recently, Long et al [24] have given novel and innovative results for the existence of a solution of some uncertain differential equations. Some more results in this direction were obtained in [25,26] and the references therein, which are expected to attract the attention of various researchers in the near future.…”

Section: Introductionmentioning

confidence: 87%

Generalized contraction principle under relatively weaker contraction in partial metric spaces

2019

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In this paper, we introduce the concept of a generalized weak (φ, R)-contraction and employ this to prove some fixed point results for self-mappings in partial metric spaces endowed with a binary relation R. We also establish some consequences in ordered partial metric spaces and metric spaces with a binary relation and exemplify that our results are a sharpened version of results of Zhiqun Xue (Nonlinear Funct.

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An extension of Krasnoselskii’s fixed point theorem and its application to nonlocal problems for implicit fractional differential systems with uncertainty

Cited by 29 publications

References 29 publications

Fuzzy delay differential equations under granular differentiability with applications

Fuzzy delay differential equations under granular differentiability with applications

Krasnoselskii N-Tupled Fixed Point Theorem with Applications to Fractional Nonlinear Dynamical System

Generalized contraction principle under relatively weaker contraction in partial metric spaces

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