Upper and Lower Solution method for Positive solution of generalized Caputo fractional differential equations

Patil, Jayshree; Chaudhari, Archana; Abdo, Mohammed S.; Hardan, Basel

doi:10.31197/atnaa.709442

Cited by 15 publications

(9 citation statements)

References 27 publications

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“…As we know, the existence theory is meat-and-potatoes in every field of science, as it is very applicative to comprehend whether there is a solution to a given differential equation beforehand; otherwise, all the attempts to find a numerical or analytic solution will become valueless. The analysis of fractional differential equations has been carried out by various authors (see, for example, [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]).…”

Section: Introductionmentioning

confidence: 99%

On solutions of nonlinear BVPs with general boundary conditions by using a generalized Riesz–Caputo operator

et al. 2021

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In this work, we study the existence, uniqueness, and continuous dependence of solutions for a class of fractional differential equations by using a generalized Riesz fractional operator. One can view the results of this work as a refinement for the existence theory of fractional differential equations with Riemann–Liouville, Caputo, and classical Riesz derivative. Some special cases can be derived to obtain corresponding existence results for fractional differential equations. We provide an illustrated example for the unique solution of our main result.

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Section: Introductionmentioning

confidence: 99%

On solutions of nonlinear BVPs with general boundary conditions by using a generalized Riesz–Caputo operator

et al. 2021

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“…Also, the model may be applied to describe the reaction of β-galactosidase [24]. The system under consideration may be further studied in the form of fractional dierential equations, such as Caputo fractional dierential equations [25,26].…”

Section: Discussionmentioning

confidence: 99%

Numerical analysis of coupled systems of ODEs and applications to enzymatic competitive inhibition by product

Mai

Nhan²

2021

Advances in the Theory of Nonlinear Analysis and Its Application

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Enzymatic inhibition is one of the key regulatory mechanisms in cellular metabolism, especially the enzymatic competitive inhibition by product. This inhibition process helps the cell regulate enzymatic activities. In this paper, we derive a mathematical model describing the enzymatic competitive inhibition by product. The model consists of a coupled system of nonlinear ordinary dierential equations for the species of interest. Using nondimensionalization analysis, a formula for product formation rate for this mechanism is obtained in a transparent manner. Further analysis for this formula yields qualitative insights into the maximal reaction velocity and apparent Michaelis-Menten constant. Integrating the model numerically, the eects of the model parameters on the model output are also investigated. Finally, a potential application of the model to realistic enzymes is briey discussed.

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“…For example, when the initial temperature or the final temperature for heat equation is not given immediately, but there is information regarding the temperature over a given period of time that can be described by a nonlocal initial condition. PDEs with nonlocal conditions were considered in many works, for example, see [25] for reaction-diffusion equations and [26][27][28][29][30][31][32][33][34][35] for some other PDEs. As we said before, there are not any results for considering our model (1.1) with the nonlocal final condition and the integral condition…”

Section: Introductionmentioning

confidence: 99%

On a time fractional diffusion with nonlocal in time conditions

Tuấn

Triet²,

Luc³

et al. 2021

Adv Differ Equ

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In this work, we consider a fractional diffusion equation with nonlocal integral condition. We give a form of the mild solution under the expression of Fourier series which contains some Mittag-Leffler functions. We present two new results. Firstly, we show the well-posedness and regularity for our problem. Secondly, we show the ill-posedness of our problem in the sense of Hadamard. Using the Fourier truncation method, we construct a regularized solution and present the convergence rate between the regularized and exact solutions.

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Upper and Lower Solution method for Positive solution of generalized Caputo fractional differential equations

Cited by 15 publications

References 27 publications

On solutions of nonlinear BVPs with general boundary conditions by using a generalized Riesz–Caputo operator

On solutions of nonlinear BVPs with general boundary conditions by using a generalized Riesz–Caputo operator

Numerical analysis of coupled systems of ODEs and applications to enzymatic competitive inhibition by product

On a time fractional diffusion with nonlocal in time conditions

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