共查询到20条相似文献,搜索用时 15 毫秒
1.
Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations 总被引:1,自引:0,他引:1
In this paper, we investigate the existence of positive solutions for the singular fractional boundary value problem: Dαu(t)+f(t,u(t),Dμu(t))=0, u(0)=u(1)=0, where 1<α<2, 0<μ?α−1, Dα is the standard Riemann-Liouville fractional derivative, f is a positive Carathéodory function and f(t,x,y) is singular at x=0. By means of a fixed point theorem on a cone, the existence of positive solutions is obtained. The proofs are based on regularization and sequential techniques. 相似文献
2.
A. V. Glushak 《Mathematical Notes》2007,82(5-6):596-607
We study the relationship between the solutions of abstract differential equations with fractional derivatives and their stability with respect to the perturbation by a bounded operator. Besides, we obtain representations for the solution of an inhomogeneous equation and for an equation containing a fractional power of the generator of a cosine operator function. 相似文献
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Nontrivial solutions of nonlocal boundary value problems for nonlinear higher-order singular fractional differential equations 下载免费PDF全文
This paper deals with the existence and multiplicity of nontrivial solutions of nonlocal boundary value problems for nonlinear higher-order singular fractional differential equations with sign-changing nonlinear term. The main tool used in the proof is topological degree theory. Some examples explain that our results cannot be obtained by the method of cone theory. 相似文献
5.
M.R. Dostani? 《Journal of Mathematical Analysis and Applications》2011,375(2):677-684
In this paper we find the first term in the asymptotics of singular values of the generalized fractional integration operator. 相似文献
6.
In this paper, we shall discuss the properties of the well-known Mittag-Leffler function, and consider the existence and uniqueness of solution of the initial value problem for fractional differential equation involving Riemann-Liouville sequential fractional derivative by using monotone iterative method. 相似文献
7.
Rabha W. Ibrahim 《Journal of Mathematical Analysis and Applications》2011,380(1):232-240
By employing majorant functions, the existence and uniqueness of holomorphic solutions to nonlinear fractional partial differential equations (the Cauchy problems) are introduced. Furthermore, the analytic continuation of solutions is studied. 相似文献
8.
利用分歧方法和拓扑度理论,研究了一类带参数的分数阶微分方程积分边值问题正解的存在性.根据格林函数的性质,得到了系统正解的存在的若干充分条件.最后,通过数值例子验证了所得结果的有效性. 相似文献
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Zhongli Wei Changci PangYouzheng Ding 《Communications in Nonlinear Science & Numerical Simulation》2012,17(8):3148-3160
In this paper, we investigate the existence of positive solutions of singular super-linear (or sub-linear) integral boundary value problems for fractional differential equation involving Caputo fractional derivative. Necessary and sufficient conditions for the existence of C3[0, 1] positive solutions are given by means of the fixed point theorems on cones. Our nonlinearity f(t, x) may be singular at t = 0 and/or t = 1. 相似文献
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In this paper, we discuss the existence of solutions for a three-point boundary value problem of fractional differential equations with nonlinear growth. By using the coincidence degree theory, we present a existence result at resonance case. 相似文献
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A. V. Glushak 《Mathematical Notes》2005,77(1-2):26-38
The uniform well-posedness of a Cauchy-type problem with two fractional derivatives and bounded operator A is proved. For an unbounded operator A we present a test for the uniform well-posedness of the problem under consideration consistent with the test for the uniform well-posedness of the Cauchy problem for an equation of second order.Translated from Matematicheskie Zametki, vol. 77, no. 1, 2005, pp. 28–41.Original Russian Text Copyright © 2005 by A. V. Glushak.This revised version was published online in April 2005 with a corrected issue number. 相似文献
15.
Analysis of a system of fractional differential equations 总被引:2,自引:0,他引:2
Varsha Daftardar-Gejji A. Babakhani 《Journal of Mathematical Analysis and Applications》2004,293(2):511-522
We prove existence and uniqueness theorems for the initial value problem for the system of fractional differential equations , where Dα denotes standard Riemann-Liouville fractional derivative, 0<α<1, and A is a square matrix. The unique solution to this initial value problem turns out to be , where Eα denotes the Mittag-Leffler function generalized for matrix arguments. Further we analyze the system , , 0<α<1, and investigate dependence of the solutions on the initial conditions. 相似文献
16.
Positive solutions for boundary value problem of nonlinear fractional differential equation 总被引:6,自引:0,他引:6
In this paper, we investigate the existence and multiplicity of positive solutions for nonlinear fractional differential equation boundary value problem:
17.
Shuqin Zhang 《Positivity》2008,12(4):711-724
In this paper, we consider the existence of nonnegative solutions of initial value problem for singular nonlinear fractional
differential equation
where D
s
and D
α are the standard Riemann-Liouville fractional derivatives, , may be change sign, t
r
a : [0,1] → R, 0 ≤ r < s − α, and λ > 0 is a parameter. Our analysis relies on the Schauder fixed point theorem.
相似文献
18.
Ravi P. Agarwal 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(6):2859-124
We consider a differential equation of fractional order with uncertainty and present the concept of solution. It extends, for example, the cases of first order ordinary differential equations and of differential equations with uncertainty. Some examples are presented. 相似文献
19.
This paper investigates the existence and uniqueness of positive solutions for a class of nonlinear fractional delay differential
equations. Using a nonlinear alternative of Leray-Schauder type, we show the existence of positive solutions for the equations
in question. 相似文献
20.
Prabir Burman 《Journal of Mathematical Analysis and Applications》2007,327(1):251-256
From the results of Dostanic [M.R. Dostanic, Asymptotic behavior of the singular values of fractional integral operators, J. Math. Anal. Appl. 175 (1993) 380-391] and V? and Gorenflo [Kim Tuan V?, R. Gorenflo, Singular values of fractional and Volterra integral operators, in: Inverse Problems and Applications to Geophysics, Industry, Medicine and Technology, Ho Chi Minh City, 1995, Ho Chi Minh City Math. Soc., Ho Chi Minh City, 1995, pp. 174-185] it is known that the jth singular value of the fractional integral operator of order α>0 is approximately (πj)−α for all large j. In this note we refine this result by obtaining sharp bounds for the singular values and use these bounds to show that the jth singular value is (πj)−α[1+O(j−1)]. 相似文献