共查询到20条相似文献,搜索用时 15 毫秒
1.
F. G. Khushtova 《Russian Mathematics (Iz VUZ)》2017,61(7):73-82
We investigate the second boundary-value problem in the half-strip for a parabolic equation with the Bessel operator and Riemann–Liouville partial derivative. In terms of the integral transformation with theWright function in the kernel, we find the representation of a solution in the case of zero edge condition. We prove the uniqueness of a solution in the class of functions satisfying an analog of the Tikhonov condition. 相似文献
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In this work, we are mainly concerned with the existence of positive solutions for the fractional boundary-value problem $$ \left\{ {\begin{array}{*{20}{c}} {D_{0+}^{\alpha }D_{0+}^{\alpha }u=f\left( {t,u,{u}^{\prime},-D_{0+}^{\alpha }u} \right),\quad t\in \left[ {0,1} \right],} \hfill \\ {u(0)={u}^{\prime}(0)={u}^{\prime}(1)=D_{0+}^{\alpha }u(0)=D_{0+}^{{\alpha +1}}u(0)=D_{0+}^{{\alpha +1}}u(1)=0.} \hfill \\ \end{array}} \right. $$ Here ?? ?? (2, 3] is a real number, $ D_{0+}^{\alpha } $ is the standard Riemann?CLiouville fractional derivative of order ??. By virtue of some inequalities associated with the fractional Green function for the above problem, without the assumption of the nonnegativity of f, we utilize the Krasnoselskii?CZabreiko fixed-point theorem to establish our main results. The interesting point lies in the fact that the nonlinear term is allowed to depend on u, u??, and $ -D_{0+}^{\alpha } $ . 相似文献
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For an equation of mixed type with a Riemann–Liouville fractional partial derivative, we prove the uniqueness and existence of a solution of a nonlocal problem whose boundary condition contains a linear combination of generalized fractional integro-differentiation operators with the Gauss hypergeometric function in the kernel. A closed-form solution of the problem is presented. 相似文献
4.
Yang Liu 《Applied Mathematics Letters》2012,25(11):1986-1992
In this work, by means of the fixed point theorem in a cone, we establish the existence result for a positive solution to a kind of boundary value problem for a nonlinear differential equation with a Riemann–Liouville fractional order derivative. An example illustrating our main result is given. Our results extend previous work in the area of boundary value problems of nonlinear fractional differential equations [C. Goodrich, Existence of a positive solution to a class of fractional differential equations, Appl. Math. Lett. 23 (2010) 1050–1055]. 相似文献
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《Chaos, solitons, and fractals》2001,12(13):2577-2587
Fractional master equations may be defined either by means of Liouville–Riemann (L–R) fractional derivative or via non-standard analysis. The first approach describes processes with long-range dependence whilst the second approach deals with processes involving independent increments. The present papers put in evidence some of the differences between these two modellings, and to this end it especially considers more fractional Poisson processes. 相似文献
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We study a nonlocal problem for a fractional partial differential equation with the Dzhrbashyan–Nersesyan fractional differentiation operator. By separation of variables, we prove a theorem on the existence and uniqueness of a regular solution of this problem. 相似文献
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The article investigates the reconstruction of the internal boundary of a two-dimensional region in the two-dimensional initial–boundary-value
problem for the homogeneous heat equation. The initial values for the determination of the internal boundary are provided
by a boundary condition of second kind on the external boundary and the solution of the initial–boundary-value problem at
finitely many points inside the region. The inverse problem is reduced to solving a system of integral equations nonlinear
in the function describing the sought boundary. An iterative numerical procedure is proposed involving linearization of integral
equations. 相似文献
10.
We study the asymptotic distribution of eigenvalues of the problem generated by the Sturm–Liouville operator equation. A formula
for the regularized trace of the corresponding operator is obtained. 相似文献
11.
A one dimensional fractional diffusion model with the Riemann–Liouville fractional derivative is studied. First, a second order discretization for this derivative is presented and then an unconditionally stable weighted average finite difference method is derived. The stability of this scheme is established by von Neumann analysis. Some numerical results are shown, which demonstrate the efficiency and convergence of the method. Additionally, some physical properties of this fractional diffusion system are simulated, which further confirm the effectiveness of our method. 相似文献
12.
For a generalized Cauchy–Riemann system whose coefficients admit higher-order singularities on a segment, we obtain an integral representation of the general solution and study a boundary value problem combining the properties of the linear conjugation problem and the Riemann–Hilbert problem in function theory. 相似文献
13.
In this paper we consider the relations between the Riemann–Hilbert monodromy problem and the matrix Riemann–Hilbert boundary-value problem with piecewise continuous coefficient and construct the so-called canonical matrix for the boundary-value problem for a piecewise continuous matrix-function. The formula for the calculation of the index is also obtained. 相似文献
14.
D. B. Davletov 《Mathematical Notes》2013,93(3-4):545-555
The Dirichlet boundary-value problem for the eigenvalues of the Lamé operator in a twodimensional bounded domain with a small hole is studied. The asymptotics of the eigenvalue of this boundary-value problem is constructed and justified up to the power of the parameter defining the diameter of the hole. 相似文献
15.
This paper is concerned with Riemann–Liouville abstract fractional Cauchy Problems with damping. The notion of Riemann–Liouville fractional (α,β,c) resolvent is developed, where 0<β<α≤1. Some of its properties are obtained. By combining such properties with the properties of general Mittag-Leffler functions, existence and uniqueness results of the strong solution of Riemann–Liouville abstract fractional Cauchy Problems with damping are established. As an application, a fractional diffusion equation with damping is presented. 相似文献
16.
R. B. Seilhanova 《Journal of Mathematical Sciences》2011,175(1):51-56
In this paper, the unique solvability of the Poincaré problem for multidimensional hyperbolic equation with the Chaplygin operator in the domain with a deviation from the characteristic is proved. In the theory of partial differential equations of the hyperbolic type, boundary-value problems with the data on the whole boundary of the domain serve as an example of problems that are not well posed [3]. 相似文献
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Gelfand’s problem on the large time asymptotics of the solution of the Cauchy problem for a first-order quasilinear equation with initial conditions of the Riemann type is considered. Exact asymptotics in the Cauchy–Gelfand problem are obtained and the initial data parameters responsible for the localization of shock waves are described on the basis of the vanishing viscosity method with uniform estimates without the a priori monotonicity assumption for the initial data. 相似文献
20.
In this paper, the fractional variational iteration method (FVIM) was applied to obtain the approximate solutions of time-fractional Swift–Hohenberg (S–H) equation with modified Riemann–Liouville derivative. A new application of fractional variational iteration method (FVIM) was extended to derive analytical solutions in the form of a series for these equations. Numerical results showed the FVIM is powerful, reliable and effective method when applied strongly nonlinear equations with modified Riemann–Liouville derivative. 相似文献