共查询到20条相似文献,搜索用时 31 毫秒
1.
Fulai Chen 《Nonlinear Analysis: Real World Applications》2012,13(1):287-298
We present some results for the global attractivity of solutions for fractional differential equations involving Riemann-Liouville fractional calculus. The results are obtained by employing Krasnoselskii’s fixed point theorem. Similar results for fractional differential equations involving Caputo fractional derivative are also obtained by using the classical Schauder’s fixed point theorem. Several examples are given to illustrate our main results. 相似文献
2.
This paper addressed the controllability of nonlinear fractional order integrodifferential systems with input delay. Firstly, the Caputo fractional derivatives and the Mittag‐Leffler functions are employed. Thereafter, we establish a set of sufficient and necessary conditions for the controllability of the linear fractional system. Furtherly, controllability conditions of the nonlinear integrodifferential fractional order system with input delay are acquired by utilizing Arzela‐Ascoli theorem and Schauder's fixed‐point theorem. Finally, an example is presented to demonstrate our main results. 相似文献
3.
4.
《数学季刊》2014,(4)
In this paper, we investigate the nonlinear fractional difference equation with nonlocal fractional boundary conditions. We derive the Green's function for this problem and show that it satisfies certain properties. Some existence results are obtained by means of nonlinear alternative of Leray-Schauder type theorem and Krasnosel-skii's fixed point theorem. 相似文献
5.
Mouffak Benchohra Naima Hamidi Johnny Henderson 《Numerical Functional Analysis & Optimization》2013,34(4):404-414
We are concerned with the existence of solutions of a class of fractional differential equations with anti-periodic boundary conditions involving the Caputo fractional derivative. We give two results: the first is based on Banach's fixed-point theorem, and the second is based on Schauder's fixed-point theorem. 相似文献
6.
Jian-gen Liu Xiao-Jun Yang Yi-Ying Feng Hong-Yi Zhang 《Journal of Applied Analysis & Computation》2020,10(3):1060-1072
Under investigation in this paper is a time fractional nonlinear diffusion equation which can be utilized to express various diffusion processes. The symmetry of this considered equation has been obtained via fractional Lie group approach with the sense of Riemann-Liouville (R-L) fractional derivative. Based on the symmetry, this equation can be changed into an ordinary differential equation of fractional order. Moreover, some new invariant solutions of this considered equation are found. Lastly, utilising the Noether theorem and the general form of Noether type theorem, the conservation laws are yielded to the time fractional nonlinear diffusion equation, respectively. Our discovery that there are no conservation laws under the general form of Noether type theorem case. This result tells us the symmetry of this equation is not variational symmetry of the considered functional. These rich results can give us more information to interpret this equation. 相似文献
7.
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
8.
Boris I. Golubov 《Analysis Mathematica》2006,32(3):173-205
Summary For the fractional dyadic derivative and integral, the following analogues of two theorems of Lebesgue are proved: the theorem
on differentiation of the indefinite Lebesgue integral of an integrable function at its Lebesgue points, and the theorem
on reconstruction of an absolutely continuous function by means of its derivative. Dyadic fractional analogues of the formula
of integration by parts are also obtained. In addition, some theorems are proved on dyadic fractional differentiation and
integration of a Lebesgue integral depending on a parameter. Most of the results are new even for dyadic derivatives and
integrals of natural order. 相似文献
9.
In this paper we study the controllability of fractional integrodifferential systems in Banach spaces. The results are obtained by using fractional calculus, semigroup theory and the fixed point theorem. 相似文献
10.
Kerboua Mourad 《随机分析与应用》2018,36(2):209-223
In this paper, the approximate controllability for Sobolev-type fractional neutral stochastic evolution equations with fractional stochastic nonlocal conditions and fractional Brownian motion in a Hilbert space are studied. The results are obtained by using semigroup theory, fractional calculus, stochastic integrals for fractional Brownian motion, Banach's fixed point theorem, and methods adopted directly from deterministic control problems for the main results. Finally, an example is given to illustrate the application of our result. 相似文献
11.
Solvability for a higher-order Hadamard fractional differential model with a sign-changing nonlinearity dependent on the parameter $\varrho$
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Until now most of the results are obtained in the sense of fractional derivatives such as Caputo and Riemann-Liouville, and there are few models using the Hadamard fractional derivatives. In this paper, based on the properties of the Green"s function, the existence of positive solutions are obtained for a Hadamard fractional differential equation with a higher-order sign-changing nonlinearity under some conditions by the fixed point theorem, and the existence of positive solutions is dependent on the parameter $\varrho$ for the Semipositive problem. 相似文献
12.
孟伟 《数学的实践与认识》2020,(8):192-198
给出了分数阶灰色累减生成算子的详细推导过程,并证明了分数阶灰色累减生成算子的不动点定理、信息优先原理、交换律与指数律,为分数阶灰色预测模型提供了理论基础.算例验证了分数阶灰色累减生成算子的特征,在灰色预测模型GM(1,1)中的应用证明了分数阶灰色累减生成算子的有效性. 相似文献
13.
We investigate impulsive fractional Langevin equation involving two fractional Caputo derivatives with boundary value conditions. By Banach contraction mapping principle and Krasnoselskii"s fixed point theorem, some results on the existence and uniqueness of solution are obtained. 相似文献
14.
Xuhuan Wang Xiuqing Guo Guosheng Tang 《Journal of Applied Mathematics and Computing》2013,41(1-2):367-375
In this paper, the existence of solutions of an anti-periodic fractional boundary value problem for nonlinear fractional differential equations is investigated. The contraction mapping principle and Leray-Schauder’s fixed point theorem are applied to establish the results. 相似文献
15.
Csar T. Ledesma Josias V. Baca J. Vanterler da C. Sousa 《Mathematical Methods in the Applied Sciences》2022,45(1):49-76
In this present paper, we discuss some properties of fractional operators with fixed memory length (Riemann–Liouville fractional integral, Riemann–Liouville and Caputo fractional derivatives). Some observations and examples are discussed during the article, in order to make the results well defined and clear. Furthermore, we consider the fundamental theorem of calculus for fractional operators with fixed memory length. 相似文献
16.
Controllability of nonlinear fractional dynamical systems 总被引:1,自引:0,他引:1
K. Balachandran 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(4):1919-1926
In this paper we establish a set of sufficient conditions for the controllability of nonlinear fractional dynamical systems. The results are obtained by using the recently derived formula for solution representation of systems of fractional differential equations and the application of the Schauder fixed point theorem. Examples are provided to illustrate the results. 相似文献
17.
In this paper, we study necessary conditions for the existence and uniqueness of continuous solution for a nonlocal boundary value problem with nonlinear term involving Riemann–Liouville fractional derivative. Our results are based on Schauder fixed point theorem and the Banach contraction principle fixed point theorem. Examples illustrating the obtained results are also presented. 相似文献
18.
In this paper,we are concerned with the existence of positive solutions to an m-point boundary value problem with p-Laplacian of nonlinear fractional differential equation.By means of Krasnosel'skii fixed-point theorem on a convex cone and Leggett-Williams fixed-point theorem,the existence results of solutions are obtained. 相似文献
19.
In this paper, we prove the existence and controllability results for fractional semilinear differential inclusions involving the Caputo derivative in Banach spaces. The results are obtained by using fractional calculation, operator semigroups and Bohnenblust–Karlin’s fixed point theorem. At last, an example is given to illustrate the theory. 相似文献
20.
In this paper, we consider the analytical solutions of multi-term time–space fractional advection–diffusion equations with mixed boundary conditions on a finite domain. The technique of spectral representation of the fractional Laplacian operator is used to convert the multi-term time–space fractional advection–diffusion equations into multi-term time fractional ordinary differential equations. By applying Luchko’s theorem to the resulting fractional ordinary differential equations, the desired analytical solutions are obtained. Our results are applied to derive the analytical solutions of some special cases to demonstrate their practical applications. 相似文献