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1.
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
2.
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
3.
《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
4.
Churong Chen Martin Bohner Baoguo Jia 《Mathematical Methods in the Applied Sciences》2019,42(18):7461-7470
We study the Ulam‐Hyers stability of linear and nonlinear nabla fractional Caputo difference equations on finite intervals. Our main tool used is a recently established generalized Gronwall inequality, which allows us to give some Ulam‐Hyers stability results of discrete fractional Caputo equations. We present two examples to illustrate our main results. 相似文献
5.
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
6.
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
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.
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
9.
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
10.
Jean‐Daniel Djida Abdon Atangana 《Numerical Methods for Partial Differential Equations》2017,33(5):1616-1627
We prove existence and uniqueness of the flow of water within a confined aquifer with fractional diffusion in space and fractional time derivative in the sense of Caputo‐Fabrizio using the classical contraction Banach theorem. We also propose the numerical approximation of the model using the Crank–Nicolson numerical scheme. To check the effectiveness of the model, stability analysis of the numerical scheme for the new model is presented.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1616–1627, 2017 相似文献
11.
Dileep Kumar Sudhakar Chaudhary V.V.K. Srinivas Kumar 《Numerical Methods for Partial Differential Equations》2019,35(6):2056-2075
This article presents a finite element scheme with Newton's method for solving the time‐fractional nonlinear diffusion equation. For time discretization, we use the fractional Crank–Nicolson scheme based on backward Euler convolution quadrature. We discuss the existence‐uniqueness results for the fully discrete problem. A new discrete fractional Gronwall type inequality for the backward Euler convolution quadrature is established. A priori error estimate for the fully discrete problem in L2(Ω) norm is derived. Numerical results based on finite element scheme are provided to validate theoretical estimates on time‐fractional nonlinear Fisher equation and Huxley equation. 相似文献
12.
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
13.
Hasib Khan Cemil Tun Wen Chen Aziz Khan 《Journal of Applied Analysis & Computation》2018,8(4):1211-1226
In this paper, we prove necessary conditions for existence and uniqueness of solution (EUS) as well Hyers-Ulam stability for a class of hybrid fractional differential equations (HFDEs) with $p$-Laplacian operator. For these aims, we take help from topological degree theory and Leray Schauder-type fixed point theorem. An example is provided to illustrate the results. 相似文献
14.
Pengfei Xu Jianhua Huang Guangan Zou 《Mathematical Methods in the Applied Sciences》2019,42(11):3818-3830
This paper is devoted to the well‐posedness for time‐space fractional Ginzburg‐Landau equation and time‐space fractional Navier‐Stokes equations by α‐stable noise. The spatial regularity and the temporal regularity of the nonlocal stochastic convolution are firstly established, and then the existence and uniqueness of the global mild solution are obtained by the Banach fixed point theorem and Mittag‐Leffler functions, respectively. Numerical simulations for time‐space fractional Ginzburg‐Landau equation are provided to verify the analysis results. 相似文献
15.
We prove some convergence theorems for α‐ψ‐pseudocontractive operators in real Hilbert spaces, by using the concept of admissible perturbation. Our results extend and complement some theorems in the existing literature. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
16.
《Numerical Functional Analysis & Optimization》2012,33(3):294-321
AbstractThis article is about Ulam’s type stability of nth order nonlinear differential equations with fractional integrable impulses. It is a best procession to the stability of higher order fractional integrable impulsive differential equations in quasi–normed Banach space. Different Ulam’s type stability results are obtained by using the definitions of Riemann–Liouville fractional integral, Hölder’s inequality and the beta integral inequality. 相似文献
17.
Hari M. Srivastava Ravi Shanker Dubey Monika Jain 《Mathematical Methods in the Applied Sciences》2019,42(13):4570-4583
Diabetes is a worldwide problem that affects one of every 11 persons nowadays. The IDF Diabetes Atlas (Eighth edition, 2017) states that approximately 415 million people in the world are living with the disease and that this number will rise to 629 million by the year 2045. It is a very serious problem of the world. A major part of the world population is affected by this disease and its resulting complications. In this paper, we propose to investigate a fractional‐order model of diabetes and its resulting complications. The mathematical model's parameters define the population of diabetic patients and those who are diabetic with complications at a given time t. We have also discussed the existence, uniqueness, and stability of the fractional‐order model, which we consider here. We make use of the homotopy decomposition method (HDM) in order to solve the problem. 相似文献
18.
Fathalla A. Rihan 《Numerical Methods for Partial Differential Equations》2010,26(6):1556-1571
This article is concerned with ?‐methods for delay parabolic partial differential equations. The methodology is extended to time‐fractional‐order parabolic partial differential equations in the sense of Caputo. The fully implicit scheme preserves delay‐independent asymptotic stability and the solution continuously depends on the time‐fractional order. Several numerical examples of interest are included to demonstrate the effectiveness of the method. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 相似文献
19.
Zhinan Xia 《Mathematical Methods in the Applied Sciences》2015,38(5):799-810
In this paper, we propose a new class of functions called pseudo ‐asymptotically ω‐periodic function in the Stepanov sense and explore its properties in Banach spaces including composition results. Furthermore, the existence and uniqueness of the pseudo ‐asymptotically ω‐periodic mild solutions to Volterra integro‐differential equations is investigated. Applications to integral equations arising in the study of heat conduction in materials with memory are shown. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
20.
In this paper, we consider the problem of approximating a given matrix with a matrix whose eigenvalues lie in some specific region Ω of the complex plane. More precisely, we consider three types of regions and their intersections: conic sectors, vertical strips, and disks. We refer to this problem as the nearest Ω‐stable matrix problem. This includes as special cases the stable matrices for continuous and discrete time linear time‐invariant systems. In order to achieve this goal, we parameterize this problem using dissipative Hamiltonian matrices and linear matrix inequalities. This leads to a reformulation of the problem with a convex feasible set. By applying a block coordinate descent method on this reformulation, we are able to compute solutions to the approximation problem, which is illustrated on some examples. 相似文献