Existence of Solutions to Fractional Differential Equations With Fractional-Order Derivative Terms

Sun, Ai; Su, You-Hui; Yuan, Qingchun; Li, Tongxiang

doi:10.11948/20200072

Cited by 10 publications

(7 citation statements)

References 22 publications

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“…Fractional differential equation is a generalization of integer-order differential equation, which can describe some complex phenomena in nature and engineering more accurately. For example, fractional differential equations provide a more appropriate model for describing diffusion processes, wave phenomena and memory effects [1][2][3][4][5][6]. In addition, fractional differential equations also show advantages in dealing with singular systems and nonlinear problems.…”

Section: Introductionmentioning

confidence: 99%

Existence and simulation of solutions for a class of fractional differential systems with p-Laplacian operators on star graphs

Zhang,

Su,

Yun

2024

Preprint

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This paper is mainly concerned with the existence and simulation of solutions for a class of Caputofractional differential systems with $p$-Laplacian operators on star graphs. The Hyers-Ulam stability of the systems on star graphsis also proved. Furthermore, an example on a formaldehyde graph is presented to demonstrate the practicality of the main results. The innovation of this paper lies in combining a fractional differential system with a formaldehyde graph, interpreting the chemical bonds as the edges of the graph, and exploring the existence and numerical simulation of solutions to the fractional differential system on this unique graph structure. MSC(2020): 34A08 , 34B15 , 34K37.

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Section: Introductionmentioning

confidence: 99%

Existence and simulation of solutions for a class of fractional differential systems with p-Laplacian operators on star graphs

Zhang,

Su,

Yun

2024

Preprint

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“…The model described by differential equations on star graphs has applications in chemical engineering, biology, physics and other fields [19][20][21][22][23]. At present, a few researchers have studied the existence results of solutions of differential equations on star graphs [24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

“…Inspired by the above work and relevant literatures [20,23,27], we will devote to consider the Ulam's stability and existence of solutions to the following fractional differential system with p-Laplacian operator on star graphs (1.1)…”

Section: Introductionmentioning

confidence: 99%

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Nan¹,

Hu²,

Su³

et al. 2023

DSA

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As we all know, star graphs are very useful in physics, chemistry, biology and other fields, but few people have studied the existence of solutions to differential system on star graphs.In this paper, we investigate the existence of solutions to a fractional differential system on star graphs with p-Laplacian operator. Ulam's stability and existence of the solutions to the fractional differential system on star graphs are proved. In addition, two examples under different background graphs (star graphs and formaldehyde graphs) and the approximation graphics for the solutions are provided to illustrate the application of our main results. The interesting point of this article is that it not only studies the existence of solutions to fractional differential system on the star graphs, but also gives approximate graphs of solutions by using the iterative methods and numerical simulation.

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“…Nowadays, some achievements have been made in the study of the existence of solutions of fractional order differential equations [30][31][32][33]. The terminal value problem is widely used in economics for risk control, dividend distribution, principal-agent and unbounded return dynamic optimization problems [34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Stability and existence of solutions to a class of Atangana-Baleanu-Caputo coupled fractional differential equations

Lin

Wei-min

et al. 2023

Preprint

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In this paper, we are concerned with the stability and existence of solutions to a class of Atangana-Baleanu-Caputo coupled fractional differential equations. The existence and uniqueness of the solution of the fractional system are obtained through Schaefer and Banach fixed point theorems, and sufficient conditions for the existence and uniqueness of the solutions are also developed. Subsequently, the Hyers-Ulam stability and generalized Hyers-Ulam stability of the solution are considered. In particular, two examples are given to illustrate the main results. The interesting aspect of this paper is that it performs numerical simulations using the monotone iterative method to verify the applicability of the system.

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Existence of Solutions to Fractional Differential Equations With Fractional-Order Derivative Terms

Cited by 10 publications

References 22 publications

Existence and simulation of solutions for a class of fractional differential systems with p-Laplacian operators on star graphs

Existence and simulation of solutions for a class of fractional differential systems with p-Laplacian operators on star graphs

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Stability and existence of solutions to a class of Atangana-Baleanu-Caputo coupled fractional differential equations

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