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1.
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
2.
Hyers–Ulam stability of nonlinear differential equations with fractional integrable impulses
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Akbar Zada Wajid Ali Syed Farina 《Mathematical Methods in the Applied Sciences》2017,40(15):5502-5514
This paper is devoted to establish Bielecki–Ulam–Hyers–Rassias stability, generalized Bielecki–Ulam–Hyers–Rassias stability, and Bielecki–Ulam–Hyers stability on a compact interval [0,T], for a class of higher‐order nonlinear differential equations with fractional integrable impulses. The phrase ‘fractional integrable’ brings one to fractional calculus. Hence, applying usual methods for analysis offers many difficulties in proving the results of existence and uniqueness of solution and stability theorems. Picard operator is applied in showing existence and uniqueness of solution. Stability results are obtained by using the tools of fractional calculus and Hölder's inequality of integration. Along with tools of fractional calculus, Bielecki's normed Banach spaces are considered, which made the results more interesting. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
3.
In this paper, we first utilize fractional calculus, the properties of classical and generalized Mittag-Leffler functions to prove the Ulam–Hyers stability of linear fractional differential equations using Laplace transform method. Meanwhile, Ulam–Hyers–Rassias stability result is obtained as a direct corollary. Finally, we apply the same techniques to discuss the Ulam’s type stability of fractional evolution equations, impulsive fractional evolutions equations and Sobolev-type fractional evolution equations. 相似文献
4.
《Mathematical Methods in the Applied Sciences》2018,41(9):3430-3440
This paper deals with 2 core aspects of fractional calculus including existence of positive solution and Hyers‐Ulam stability for a class of singular fractional differential equations with nonlinear p‐Laplacian operator in Caputo sense. For these aims, the suggested problem is converted into an integral equation via Green function , for ε∈(n−1,n], where n≥4. Then, the Green function is examined whether it is increasing or decreasing and positive or negative function. After these properties, some classical fixed‐point theorems are used for the existence of positive solution. Hyers‐Ulam stability of the proposed problem is also considered. For the application of the results, an expressive example is included. 相似文献
5.
Akbar Zada Shaleena Shaleena Tongxing Li 《Mathematical Methods in the Applied Sciences》2019,42(4):1151-1166
In this paper, we interrogate different Ulam type stabilities, ie, β–Ulam–Hyers stability, generalized β–Ulam–Hyers stability, β–Ulam–Hyers–Rassias stability, and generalized β–Ulam–Hyers–Rassias stability, for nth order nonlinear differential equations with integrable impulses of fractional type. The existence and uniqueness of solutions are investigated by using the Banach contraction principle. In the end, we give an example to support our main result. 相似文献
6.
JinRong Wang LinLi Lv Yong Zhou 《Communications in Nonlinear Science & Numerical Simulation》2012,17(6):2530-2538
In this paper, some new concepts in stability of fractional differential equations are offered from different perspectives. Hyers–Ulam–Rassias stability as well as Hyers–Ulam stability of a certain fractional differential equation are presented. The techniques rely on a fixed point theorem in a generalized complete metric space. Some applications of our results are also provided. 相似文献
7.
Yongshun Zhao Shurong Sun Yongxiang Zhang 《Journal of Applied Mathematics and Computing》2017,53(1-2):183-199
In this paper, we investigate existence and generalized Hyers–Ulam–Rassias stability of Stieltjes quadratic functional integral equations. Firstly, we show some basic properties of the composite function of bounded variation. Secondly, we derive the generalized Hyers–Ulam–Rassias stability result after examining the existence and uniqueness results via the theory of measure of noncompactness and a fixed point theorem of Darbo type. Finally, two examples of functional integral equations of fractional order are given to demonstrate the applicability of our results. 相似文献
8.
Hasib Khan Yongjin Li Aftab Khan Aziz Khan 《Mathematical Methods in the Applied Sciences》2019,42(9):3377-3387
In the literature, many researchers have studied Lotka‐Volterra (L‐V) models for different types of studies. In order to continue the study, we consider a fractional‐order L‐V model involving three different species in the Atangana‐Baleanu‐Caputo (ABC) sense of fractional derivative. This new model has potentials for a large number of research‐oriented studies. The first point that arises is whether the new model has a solution or not. Therefore, to answer this question, we consider the existence and uniqueness (EU) of the solutions and then Hyers‐Ulam (HU) stability for the proposed L‐V model. 相似文献
9.
Ashwini D. Mali Kishor D. Kucche 《Mathematical Methods in the Applied Sciences》2020,43(15):8608-8631
In this paper, we derive the equivalent fractional integral equation to the nonlinear implicit fractional differential equations involving Ψ-Hilfer fractional derivative subject to nonlocal fractional integral boundary conditions. The existence of a solution, Ulam–Hyers, and Ulam–Hyers–Rassias stability have been acquired by means of an equivalent fractional integral equation. Our investigations depend on the fixed-point theorem due to Krasnoselskii and the Gronwall inequality involving Ψ-Riemann–Liouville fractional integral. Finally, examples are provided to show the utilization of primary outcomes. 相似文献
10.
Samina Kamal Shah Rahmat Ali Khan Dumitru Baleanu 《Mathematical Methods in the Applied Sciences》2019,42(6):2033-2042
In this paper, the first purpose is to study existence and uniqueness of solutions to a system of implicit fractional differential equations (IFDEs) equipped with antiperiodic boundary conditions (BCs). To obtain the mentioned results, we use Schauder's and Banach fixed point theorem. The second purpose is discussing the Ulam‐Hyers (UH) and generalized Ulam‐Hyers (GUH) stabilities for the respective solutions. An example is provided to illustrate the established results. 相似文献
11.
Jae Young CHUNG 《数学学报(英文版)》2007,23(11):2017-2026
We consider a class of n-dimensional Pompeiu equations and that of Pexider equations and their Hyers Ulam stability problems in the spaces of Schwartz distributions. First, reducing the given distribution version of functional equations to differential equations we find their solutions. Secondly, using approximate identities we prove the Hyers Ulam stability of the equations. 相似文献
12.
Jos Vanterler da C. Sousa Fabio G. Rodrigues Edmundo Capelas de Oliveira 《Mathematical Methods in the Applied Sciences》2019,42(9):3033-3043
In this paper, using the Riemann‐Liouville fractional integral with respect to another function and the ψ?Hilfer fractional derivative, we propose a fractional Volterra integral equation and the fractional Volterra integro‐differential equation. In this sense, for this new fractional Volterra integro‐differential equation, we study the Ulam‐Hyers stability and, also, the fractional Volterra integral equation in the Banach space, by means of the Banach fixed‐point theorem. As an application, we present the Ulam‐Hyers stability using the α‐resolvent operator in the Sobolev space . 相似文献
13.
Dong Zhang 《Aequationes Mathematicae》2016,90(3):559-568
We propose a new approach called Hyers–Ulam programming to discriminate whether a generalized linear functional equation, with the form \({\sum_{i=1}^m L_if(\sum_{j=1}^n a_{ij}x_j) = 0}\) for functions from a normed space into a Banach space, has the Hyers–Ulam stability or not. Our main result is that if the induced Hyers–Ulam programming has a solution, then the corresponding functional equation possesses the Hyers–Ulam stability. 相似文献
14.
In the present paper we investigate some uniqueness and Ulam’s type stability concepts of fixed point equations due to Rus, for the Darboux problem of partial differential and integro-differential equations involving the Caputo fractional derivative. Our results are obtained by using weakly Picard operators theory. 相似文献
15.
John Michael Rassias 《Journal of Mathematical Analysis and Applications》2009,356(1):302-309
In 1940 S.M. Ulam proposed the famous Ulam stability problem. In 1941 D.H. Hyers solved the well-known Ulam stability problem for additive mappings subject to the Hyers condition on approximately additive mappings. The first author of this paper investigated the Hyers-Ulam stability of Cauchy and Jensen type additive mappings. In this paper we generalize results obtained for Jensen type mappings and establish new theorems about the Hyers-Ulam stability for general additive functional equations in quasi-β-normed spaces. 相似文献
16.
Jos Vanterler da Costa Sousa Daniela dos Santos Oliveira Edmundo Capelas de Oliveira 《Mathematical Methods in the Applied Sciences》2019,42(4):1249-1261
In this paper, by means of Banach fixed point theorem, we investigate the existence and Ulam–Hyers–Rassias stability of the noninstantaneous impulsive integrodifferential equation by means of ψ‐Hilfer fractional derivative. In this sense, some examples are presented, in order to consolidate the results obtained. 相似文献
17.
The purpose of this article is to generalize the theory of stability of functional equations to the case of n‐Banach spaces. In this article, we prove the generalized Hyers–Ulam stabilities of the Cauchy functional equations, Jensen functional equations and quadratic functional equations on n‐Banach spaces. 相似文献
18.
In 1940, Ulam proposed the famous Ulam stability problem. In 1941, Hyers solved the well-known Ulam stability problem for additive mappings subject to the Hyers condition on approximately additive mappings. In 2003–2006, the last author of this paper investigated the Hyers–Ulam stability of additive and Jensen type mappings. In this paper, we improve results obtained in 2003 and 2005 for Jensen type mappings and establish new theorems about the Ulam stability of additive and alternative additive mappings. These stability results can be applied in stochastic analysis, financial and actuarial mathematics, as well as in psychology and sociology. 相似文献
19.
Ajda Fo?ner 《Aequationes Mathematicae》2012,84(1-2):91-98
We study the generalized Hyers–Ulam stability of functional equations of module left (m, n)-derivations. 相似文献
20.
John Michael Rassias 《Bulletin des Sciences Mathématiques》2007,131(1):89
In 1940 S.M. Ulam proposed the famous Ulam stability problem. In 1941 D.H. Hyers solved this problem for additive mappings subject to the Hyers condition on approximately additive mappings. In this paper we generalize the Hyers result for the Ulam stability problem for Jensen type mappings, by considering approximately Jensen type mappings satisfying conditions weaker than the Hyers condition, in terms of products of powers of norms. This process leads to a refinement of the well-known Hyers-Ulam approximation for the Ulam stability problem. Besides we introduce additive mappings of the first and second form and investigate pertinent stability results for these mappings. Also we introduce approximately Jensen type mappings and prove that these mappings can be exactly Jensen type, respectively. These stability results can be applied in stochastic analysis, financial and actuarial mathematics, as well as in psychology and sociology. 相似文献