Application of piecewise fractional differential equation to COVID-19 infection dynamics

Li, Xiaoping; Alrihieli, Haifaa F.; Algehyne, Ebrahem A.; Khan, Muhammad Altaf; Alshahrani, Mohammad Y.; Alraey, Yasser; Riaz, Muhammad Bilal

doi:10.1016/j.rinp.2022.105685

Cited by 13 publications

(5 citation statements)

References 43 publications

(39 reference statements)

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“…Combining ( 8), (12), and applying Lemma 1, we conclude that BVP (1) has at least one positive solution x λ ∈ Ω 2 \ Ω 1 satisfying (6) for any λ ∈ (0, λ * ).…”

Section: Existence Multiplicity and Nonexistencementioning

confidence: 77%

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Monotone Positive Solutions for Nonlinear Fractional Differential Equations with a Disturbance Parameter on the Infinite Interval

Zheng,

Yang,

Wang

2024

Mathematics

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This paper is concerned with the existence and multiplicity of monotone positive solutions for a class of nonlinear fractional differential equation with a disturbance parameter in the integral boundary conditions on the infinite interval. By using Guo–Krasnosel’skii fixed-point theorem and the analytic technique, we divide the range of parameter for the existence of at least two, one and no positive solutions for the problem. In the end, an example is given to illustrate our main results.

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“…Combining ( 8), (12), and applying Lemma 1, we conclude that BVP (1) has at least one positive solution x λ ∈ Ω 2 \ Ω 1 satisfying (6) for any λ ∈ (0, λ * ).…”

Section: Existence Multiplicity and Nonexistencementioning

confidence: 77%

“…In recent ten years, fractional differential equations have been extensively studied, and significant achievements have been made in both theory and application; see [1][2][3][4][5][6][7][8][9][10][11][12] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Monotone Positive Solutions for Nonlinear Fractional Differential Equations with a Disturbance Parameter on the Infinite Interval

Zheng,

Yang,

Wang

2024

Mathematics

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“…Therefore, the mathematical models based on Caputo fractional derivative generalize the corresponding models based on the classical derivative and can describe better certain real-world phenomena. In particular, the boundary-value problems for systems of differential equations with the Caputo fractional derivative describe the behavior of a damping model in mechanics [ 11 ], a model for the amount of pollution in lakes connected with some rivers [ 12 ], a model to study the COVID-19 infection [ 13 ], a world population growth model, a model of a tape counter readings at an instant time [ 14 ], etc.…”

Section: Introductionmentioning

confidence: 99%

Fredholm boundary-value problem for the system of fractional differential equations

Boichuk

Feruk

2023

Nonlinear Dyn

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This paper deals with the study of Fredholm boundary-value problem for the system of fractional differential equations with Caputo derivative. The boundary-value problem is specified by linear vector functional such that the number of it components does not coincide with the dimension of the system of fractional differential equations. We first considered the general solution of the system of fractional differential equations that consist with the general solution of the associated homogeneous system and the arbitrary particular solution of the inhomogeneous system. The particular solution we found is a solution of the system of linear Volterra integral equations of the second kind with weakly singular kernels. Further, by using the theory of pseudo-inverse matrices, we established conditions that should be imposed on the coefficients of the original problem to guarantee that the indicated boundary conditions are satisfied. Moreover, a family of linearly independent solutions of this boundary-value problem is constructed. The specific examples are provided to verify the effectiveness of the proposed approach.

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“…Also, the theory of FFDEs is often used in applied sciences. The model with discrete memory effect is studied in [15][16][17]; the pantograph-type model from electrodynamics is investigated in [15,18,19]; mathematical model for studying the COVID-19 infection described by piecewise fractional differential equations is considered in [20]. The present paper is motivated mainly by [11,13].…”

Section: Introductionmentioning

confidence: 99%

Precise Conditions on the Unique Solvability of the Linear Fractional Functional Differential Equations Related to the ς-Nonpositive Operators

Dilna

2023

Fractal Fract

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Application of piecewise fractional differential equation to COVID-19 infection dynamics

Cited by 13 publications

References 43 publications

Monotone Positive Solutions for Nonlinear Fractional Differential Equations with a Disturbance Parameter on the Infinite Interval

Monotone Positive Solutions for Nonlinear Fractional Differential Equations with a Disturbance Parameter on the Infinite Interval

Fredholm boundary-value problem for the system of fractional differential equations

Precise Conditions on the Unique Solvability of the Linear Fractional Functional Differential Equations Related to the ς-Nonpositive Operators

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