On the Stability of Incommensurate h-Nabla Fractional-Order Difference Systems

Djenina, Noureddine; Ouannas, Adel; Oussaeif, Taki-Eddine; Grassi, Giuseppe; Batiha, Iqbal M.; Momani, Shaher; Albadarneh, Ramzi B.

doi:10.3390/fractalfract6030158

Cited by 13 publications

(5 citation statements)

References 20 publications

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“…By combining the above assertion with (18), we obtain (8). Thus, the existence and uniqueness of a family of functions u i ( α) are hold for ( 8) and ( 9), for i = 1, 2, • • • , ∞.…”

Section: Application Of Sentinel Methodsmentioning

confidence: 75%

“…Mathematical modeling is a method that represents and explains a lot of real phenomena using proper mathematical formulas and approaches [1][2][3][4][5]. It can be described by a set of ordinary, partial and fractional differential equations [6][7][8][9][10]. In 1795, Gauss and Legendre elaborated the method of least square, which is the most popular parameter identification technique in mathematical modelling.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On sentinel method of one-phase Stefan problem

Lamya,

Batiha,

Rezzoug

et al. 2023

J. Nig. Soc. Phys. Sci.

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This paper is interested in studying the one-phase Stefan problem. For this purpose, we use the nonlinear sentinel method, which relies typically on the approximate controllability and the Fanchel-Rockafellar duality of the minimization problem, to prove the existence and uniqueness of a solution to this problem. In particular, our research focuses on the application of the nonlinear sentinel method to the single-phase Stefan problem. This approach aids in identifying an unspecified boundary section within the domain undergoing a liquid-solid phase transition. We track the evolution of the temperature profile in the liquid-solid material and the corresponding movement of its interface over time. Eventually, the local convergence used for the iterative numerical scheme is demonstrated.

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Section: Application Of Sentinel Methodsmentioning

confidence: 75%

Section: Introductionmentioning

confidence: 99%

On sentinel method of one-phase Stefan problem

Lamya,

Batiha,

Rezzoug

et al. 2023

J. Nig. Soc. Phys. Sci.

View full text Add to dashboard Cite

show abstract

“…According to condition (7), 2r < 1. Furthermore, based on the discrete Grönwall inequality (Lemma 2) and 2r < 1, it can be obtained easily that (11) implies the following inequality:…”

Section: Resultsmentioning

confidence: 99%

“…Furthermore, fractionalorder discrete-time dynamics systems have also emerged with affluent results. For example, the stability of fractional-order difference systems have been discussed in [9][10][11], and many researchers have handled a lot of contents about different types of fractional-order difference operators [9,12].…”

Section: Introductionmentioning

confidence: 99%

Finite-Time Stability for Caputo Nabla Fractional-Order Switched Linear Systems

Long

Wang

et al. 2022

Fractal Fract

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In this paper, we address the finite-time stability problem of Caputo nabla fractional-order switched linear systems with α∈(0,1). Firstly, the monotonicity of the discrete Mittag-Leffler function is proposed. Secondly, under the per-designed switching rules, the form of the solution for Caputo nabla fractional-order switched linear systems is obtained by using the discrete unit step function. On the above basis, some sufficient conditions of finite-time stability for Caputo nabla fractional-order switched linear systems are proposed, according to the discrete Grönwall inequality and the monotonicity of the discrete Mittag-Leffler function. Finally, simulation verification is carried out via three numerical examples.

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“…The stability of the system from System ( 14) was studied in [33], in which the authors mention the following theorem: Theorem 2 ([33]). Let M be the lowest common multiple (LCM) of the denominators u i of α i 's, where…”

Section: Stability Analysis Of the Disease-free Fixed Pointmentioning

confidence: 99%

A New Incommensurate Fractional-Order Discrete COVID-19 Model with Vaccinated Individuals Compartment

et al. 2022

Self Cite

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Fractional-order systems have proved to be accurate in describing the spread of the COVID-19 pandemic by virtue of their capability to include the memory effects into the system dynamics. This manuscript presents a novel fractional discrete-time COVID-19 model that includes the number of vaccinated individuals as an additional state variable in the system equations. The paper shows that the proposed compartment model, described by difference equations, has two fixed points, i.e., a disease-free fixed point and an epidemic fixed point. A new theorem is proven which highlights that the pandemic disappears when an inequality involving the percentage of the population in quarantine is satisfied. Finally, numerical simulations are carried out to show that the proposed incommensurate fractional-order model is effective in describing the spread of the COVID-19 pandemic.

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On the Stability of Incommensurate h-Nabla Fractional-Order Difference Systems

Cited by 13 publications

References 20 publications

On sentinel method of one-phase Stefan problem

On sentinel method of one-phase Stefan problem

Finite-Time Stability for Caputo Nabla Fractional-Order Switched Linear Systems

A New Incommensurate Fractional-Order Discrete COVID-19 Model with Vaccinated Individuals Compartment

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