共查询到20条相似文献，搜索用时 15 毫秒
1.
The study of delay-fractional differential equations (fractional DEs) have recently attracted a lot of attention from scientists working on many different subjects dealing with mathematically modeling. In the study of fractional DEs the first question one might raise is whether the problem has a solution or not. Also, whether the problem is stable or not? In order to ensure the answer to these questions, we discuss the existence and uniqueness of solutions (EUS) and Hyers-Ulam stability (HUS) for our proposed problem, a nonlinear fractional DE with $p$-Laplacian operator and a non zero delay $tau>0$ of order $n-1相似文献
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本文研究了一类Caputo分数阶中立型系统.利用分步法,获得了该系统的初值问题的存在唯一性结果,再利用Gronwall不等式,证明了该系统的有限时间稳定性. 相似文献
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Jyoti P. Kharade Kishor D. Kucche 《Mathematical Methods in the Applied Sciences》2020,43(4):1938-1952
In this paper, we investigate the existence and uniqueness of solutions and derive the Ulam-Hyers-Mittag-Leffler stability results for impulsive implicit Ψ-Hilfer fractional differential equations with time delay. It is demonstrated that the Ulam-Hyers and generalized Ulam-Hyers stability are the specific cases of Ulam-Hyers-Mittag-Leffler stability. Extended version of the Gronwall inequality, abstract Gronwall lemma, and Picard operator theory are the primary devices in our investigation. We provide an example to illustrate the obtained results. 相似文献
4.
S. Naveen;V. Parthiban; 《Mathematical Methods in the Applied Sciences》2024,47(4):2981-2992
This paper presents the computational analysis of fractional differential equations of variable-order delay systems. To the proposed problem, the existence of solutions is derived using Arzela-Ascoli theorem, and the Banach fixed point theorem is used for uniqueness results. To investigate and address the computational solutions, Adams-Bashforth-Moulton technique is established. To demonstrate the method's efficiency, computational simulations of chaotic behaviors in several one-dimensional delayed systems with distinct variable orders are employed. The numerical solution of the proposed problem gives high precision approximations. 相似文献
5.
The increase of sea surface temperature in ocean changes the photosynthetic production rate of phytoplankton. Therefore, it is crucial to understand the relation between temperature and phytoplanktons photosynthesis to deal the extinction caused by excessive increase in temperature. It is worth observing that temperature is one of the most principal limiting factors for phytoplanktons production due to photosynthetic enzymes work at their optimum temperature levels. In this study, the fractional oxygen-phytoplankton-zooplankton model is considered by singular and nonsingular fractional operators within Caputo, Caputo-Fabrizio, and Atangana-Baleanu in Caputo sense. The rate of oxygen production is considered by a function of temperature account for the sea surface warming. At first, the temperature function is constant and then it starts to increase, after a certain time of increase, before the oxygen depletion begins, the temperature is set to a higher secure value. With this temperature function choice, detailed numerical simulations are carried out to provide details of the internal structure of the system. We observe that the species are more sustainable in Caputo model than its corresponding integer-order model. 相似文献
6.
This paper determines the solvability of multipoint boundary value problems for p-Laplacian generalized fractional differential systems with Riesz–Caputo derivative, which exhibits two-sided nonlocal memory effects. An equivalent integral form for the generalized fractional differential system is deduced by transformation. First, we obtain the existence of solutions on the basis of the upper–lower solutions method, in which an explicit iterative approach for approximating the solution is established. Second, we deal with a special case of our fractional differential system; in order to obtain novel results, an abstract sum-type operator equation A(x,x)+Bx+e=x on ordered Banach space is discussed. Without requiring the existence of upper–lower solutions or compactness conditions, we get several unique results of solutions for this operator equation, which provide new inspiration for the study of boundary value problems. Then, we apply these abstract results to get the uniqueness of solutions for our differential system. 相似文献
7.
This paper is concerned with a nonlinear fractional boundary value problem on a star graph. By using a transformation, the suggested problem is converted into an equivalent system of fractional boundary value problem. Schaefer's fixed point theorem and Banach's contraction principle is used to establish its existence and uniqueness results. Further, different kinds of Ulam's type stability results for the proposed problem have been discussed. Finally, two examples are presented to illustrate the application of the obtained results. 相似文献
8.
JinRong Wang Akbar Zada Hira Waheed 《Mathematical Methods in the Applied Sciences》2019,42(18):6706-6732
In this article, we study the existence and uniqueness of solution for a coupled system of nonlinear implicit fractional anti‐periodic boundary value problem. Further, we investigate different kinds of stability such as Ulam‐Hyers stability, generalized Ulam‐Hyers stability, Ulam‐Hyers‐Rassias stability, and generalized Ulam‐Hyers‐Rassias stability. We develop conditions for existence and uniqueness by using the classical fixed point theorem. Also, two examples are provided to illustrate the obtained results. 相似文献
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This paper provides a robust convergence checking method for nonlinear differential equations of fractional order with consideration of homotopy perturbation technique. The differential operators are taken in the Caputo sense. Some theorems to prove the existence and uniqueness of the series solutions are presented. Results show that the proposed theoretical analysis is accurate. 相似文献
11.
This study gives some new existence results for a three point boundary value problem involving a nonlinear fractional differential equation that incorporates a broad form of the Caputo fractional derivative concerning a new function. Our approach rests upon the fixed point theorems established by Banach, Schafer, and Schauder. Additionally, we substantiate the robustness of our findings by providing an apt illustrative example. 相似文献
12.
Muhammad Sher Kamal Shah John Rassias 《Mathematical Methods in the Applied Sciences》2020,43(10):6464-6475
13.
In this paper, we study existence and uniqueness of solutions to nonlinear three point boundary value problems for fractional differential equation of the type c D δ 0+ u(t) = f (t, u(t), c D σ 0+ u(t)), t ∈ [0, T ], u(0) = αu(η), u(T ) = βu(η), where 1 < δ < 2, 0 < σ < 1, α, β∈ R, η∈ (0, T ), αη(1 -β) + (1-α)(T βη) = 0 and c D δ 0+ , c D σ 0+ are the Caputo fractional derivatives. We use Schauder fixed point theorem and contraction mapping principle to obtain existence and uniqueness results. Examples are also included to show the applicability of our results. 相似文献
14.
Ismail T. Huseynov;Nazim I. Mahmudov; 《Mathematical Methods in the Applied Sciences》2024,47(13):11019-11043
In this paper, we consider a Cauchy problem for a Caputo-type time delay linear system of fractional differential equations with permutable matrices. First, we provide a new representation of solutions to linear homogeneous fractional differential equations using the Laplace integral transform and variation of constants formula via a newly defined delayed Mittag-Leffler type matrix function introduced through a three-parameter Mittag-Leffler function. Second, with the help of a delayed perturbation of a Mittag-Leffler type matrix function, we attain an explicit formula for solutions to a linear nonhomogeneous time delay fractional order system using the superposition principle. Furthermore, we prove the existence and uniqueness of solutions to nonlinear fractional delay differential equations using the contraction mapping principle. Finally, we present an example to illustrate the applicability of our results. 相似文献
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A. I. Gerasimov V. N. Razzhevaikin 《Computational Mathematics and Mathematical Physics》2008,48(8):1406-1417
Mathematical parasite-host models are generalized to the case when the population members differ in susceptibility and contagiousness, there is an external source of infection, and the model parameters depend periodically (seasonally) on time. The model is proved to have a periodic solution that is unique and exponentially stable for sufficiently small periodic oscillations of the coefficients. 相似文献
17.
Xiaogang Liu 《Annals of Differential Equations》2014,(2):157-165
A class of nonlinear fractional order differential equations with delay is investigated in this paper. Using Leray-Schauder fixed point theorem and the contraction mapping theorem, we obtain some sufficient conditions for the existence and uniqueness of solutions to the fractional order differential equations. 相似文献
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In this paper, we prove the existence and non-existence of solutions to two impulsive fractional differential equations with strong or weak Caputo derivatives in Euclidean space, respectively. 相似文献
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In this article, we investigate a nonlinear system of differential equations with two parameters$$left{ begin{array}{l} x\"(t)=a(t)x(t)-lambda f(t, x(t), y(t)),y\"(t)=-b(t)y(t)+mu g(t, x(t), y(t)),end{array}right.$$where $a,b in C(textbf{R},textbf{R}_+)$ are $omega-$periodic for some period $omega > 0$, $a,b notequiv 0$, $f,g in C(textbf{R} times textbf{R}_+ times textbf{R}_+ ,textbf{R}_+)$ are $omega-$periodic functions in $t$, $lambda$ and $mu$ are positive parameters. Based upon a new fixed point theorem, we establish sufficient conditions for the existence and uniqueness of positive periodic solutions to this system for any fixed $lambda,mu>0$. Finally, we give a simple example to illustrate our main result. 相似文献