Existence and uniqueness results for a nonlinear coupled system involving Caputo fractional derivatives with a new kind of coupled boundary conditions

Ahmad, Bashir; Alghanmi, Madeaha; Alsaedi, Ahmed; Nieto, Juan J.

doi:10.1016/j.aml.2021.107018

Cited by 39 publications

(23 citation statements)

References 20 publications

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“…Boundary value conditions imposed on u at 0 and T have some symmetry characteristics. By using the contraction mapping principle, we also obtain the uniqueness of the solution of problem (8). Our results include and extend some existing results (see the Section 5 for detail).…”

Section: Introductionsupporting

confidence: 73%

The Unique Solution for Sequential Fractional Differential Equations with Integral Multi-Point and Anti-Periodic Type Boundary Conditions

Hao

Chen

2022

Symmetry

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Section: Introductionsupporting

confidence: 73%

The Unique Solution for Sequential Fractional Differential Equations with Integral Multi-Point and Anti-Periodic Type Boundary Conditions

Hao

Chen

2022

Symmetry

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“…In Algorithm 2, we take tol = 10 −5 . We would like to point out that Algorithm 2 is also suitable for solving other types of boundary value problems (see, e.g., [34,35]).…”

Section: Local Testmentioning

confidence: 99%

A temporal multiscale method and its analysis for a system of fractional differential equations

Wang¹,

Lin²

2022

Preprint

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In this paper, a nonlinear system of fractional ordinary differential equations with multiple scales in time is investigated. We are interested in the effective long-term computation of the solution. The main challenge is how to obtain the solution of the coupled problem at a lower computational cost. We analysize a multiscale method for the nonlinear system where the fast system has a periodic applied force and the slow equation contains fractional derivatives as a simplication of the atherosclerosis with a plaque growth. A local periodic equation is derived to approximate the original system and the error estimates are given. Then a finite difference method is designed to approximate the original and the approximate problems. We construct four examples, including three with exact solutions and one following the original problem setting, to test the accuracy and computational efficiency of the proposed method. It is observed that, the computational time is very much reduced and the multiscale method performs very well in comparison to fully resolved simulation for the case of small time scale separation. The larger the time scale separation is, the more effective the multiscale method is.

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“…The modern methods of functional analysis areof great support in achieving existence and uniqueness results for these problems [5,6]. For some recent works on fractional or sequential fractional differential equations with nonlocal integral boundary conditions, we refer the reader to a series of papers [7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Existence Results for Coupled Nonlinear Sequential Fractional Differential Equations with Coupled Riemann–Stieltjes Integro-Multipoint Boundary Conditions

et al. 2022

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Existence and uniqueness results for a nonlinear coupled system involving Caputo fractional derivatives with a new kind of coupled boundary conditions

Cited by 39 publications

References 20 publications

The Unique Solution for Sequential Fractional Differential Equations with Integral Multi-Point and Anti-Periodic Type Boundary Conditions

The Unique Solution for Sequential Fractional Differential Equations with Integral Multi-Point and Anti-Periodic Type Boundary Conditions

A temporal multiscale method and its analysis for a system of fractional differential equations

Existence Results for Coupled Nonlinear Sequential Fractional Differential Equations with Coupled Riemann–Stieltjes Integro-Multipoint Boundary Conditions

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