共查询到20条相似文献,搜索用时 93 毫秒
1.
We construct the solution of the fractional space-time equations that describe the vibrations of a quasi-one-dimensional fractal
elastic string. We give the solution of the Cauchy problem for fractional differential equations with initial conditions.
We carry out a numerical analysis and construct the graphic variation of the displacement function of a fractal elastic string.
Three figures. Bibliography: 7 titles.
Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 26, 1996, pp. 142–147 相似文献
2.
In this paper, we consider a Cauchy problem of the time fractional diffusion equation (TFDE). Such problem is obtained from
the classical diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative of order
α (0 < α ≤ 1). We show that the Cauchy problem of TFDE is severely ill-posed and further apply a new regularization method to solve
it based on the solution given by the Fourier method. Convergence estimates in the interior and on the boundary of solution
domain are obtained respectively under different a-priori bound assumptions for the exact solution and suitable choices of
regularization parameters. Finally, numerical examples are given to show that the proposed numerical method is effective. 相似文献
3.
JinRong Wang Michal Fec˘kan Yong Zhou 《Communications in Nonlinear Science & Numerical Simulation》2013,18(2):246-256
Using the final value theorem of Laplace transform, it is firstly shown that nonhomogeneous fractional Cauchy problem does not have nonzero periodic solution. Secondly, two basic existence and uniqueness results for asymptotically periodic solution of semilinear fractional Cauchy problem in an asymptotically periodic functions space. Furthermore, existence and uniqueness results are extended to a closed, nonempty and convex set which is a subset of a Fréchet space. Some examples are given to illustrate the results. 相似文献
4.
This paper is concerned with fractional abstract Cauchy problems with order \({\alpha\in(1,2)}\). The notion of fractional solution operator is introduced, its some properties are obtained. A generation theorem for exponentially bounded fractional solution operators is given. It is proved that the homogeneous fractional Cauchy problem (FACP 0) is well-posed if and only if its coefficient operator A generates an α-order fractional solution operator. Sufficient conditions are given to guarantee the existence and uniqueness of mild solutions and strong solutions of the inhomogeneous fractional Cauchy problem (FACP f ). 相似文献
5.
G.H. Zheng 《Journal of Computational and Applied Mathematics》2010,233(10):2631-4094
In this paper, a Cauchy problem for the time fractional advection-dispersion equation (TFADE) is investigated. Such a problem is obtained from the classical advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order . We show that the Cauchy problem of TFADE is severely ill-posed and further apply a spectral regularization method to solve it based on the solution given by the Fourier method. The convergence estimate is obtained under a priori bound assumptions for the exact solution. Numerical examples are given to show the effectiveness of the proposed numerical method. 相似文献
6.
This paper is concerned with developing an operator theory for Riemann‐Liouville fractional Cauchy problem. Two notions, named Riemann‐Liouville fractional resolvent and solution operator, are developed. Some of their properties are deduced. Moreover, the obtained results are applied to Riemann‐Liouville fractional Cauchy problem. 相似文献
7.
We are interested in approximating the solution of a first-order quasi-linear equation associated with a forced unilateral obstacle condition. With this view, we make use of the time-splitting method developed classically to compute discontinuous solutions of nonhomogeneous scalar conservation laws. Here, one proves that this fractional step method converges in L1 to the weak entropy solution of the considered obstacle problem. In the case of the Cauchy problem, an L1-error bound in
is established. 相似文献
8.
In a Banach space, we consider a Cauchy type problem with a left Hadamard fractional derivative of order α ∈ (0, 1) and a Cauchy problem with a regularized Hadamard fractional derivative. We prove the well-posed solvability of such
problems with a bounded operator as well as with the generator of a strongly continuous semigroup. For inverse coefficient
problems, we indicate sufficient conditions for their unique solvability. 相似文献
9.
10.
This paper is devoted to proving the existence and uniqueness of solutions to Cauchy type problems for fractional differential equations with composite fractional derivative operator on a finite interval of the real axis in spaces of summable functions. An approach based on the equivalence of the nonlinear Cauchy type problem to a nonlinear Volterra integral equation of the second kind and applying a variant of the Banach’s fixed point theorem to prove uniqueness and existence of the solution is presented. The Cauchy type problems for integro-differential equations of Volterra type with composite fractional derivative operator, which contain the generalized Mittag-Leffler function in the kernel, are considered. Using the method of successive approximation, and the Laplace transform method, explicit solutions of the open problem proposed by Srivastava and Tomovski (2009) [11] are established in terms of the multinomial Mittag-Leffler function. 相似文献
11.
Sh. T. Karimov 《Russian Mathematics (Iz VUZ)》2017,61(8):22-35
We study the Cauchy problem for an equation with singular Bessel operator. Unlike traditional methods to solve this problem, we apply Erde´ lyi–Kober fractional operator and find an explicit formula for the desired solution. We prove that the resulting formula is a unique classical solution to the problem. 相似文献
12.
Sanja Konjik 《Journal of Mathematical Analysis and Applications》2010,365(1):259-268
Classical wave equation is generalized for the case of viscoelastic materials obeying fractional Zener model instead of Hooke's law. Cauchy problem for such an equation is studied: existence and uniqueness of the fundamental solution is proven and solution is calculated. 相似文献
13.
Rafal Kamocki 《Mathematical Methods in the Applied Sciences》2014,37(11):1668-1686
In the paper, fractional systems with Riemann–Liouville derivatives are studied. A theorem on the existence and uniqueness of a solution of a fractional ordinary Cauchy problem is given. Next, the Pontryagin maximum principle for nonlinear fractional control systems with a nonlinear integral performance index is proved. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
14.
Ahmed M.A El-Sayed 《Journal of Mathematical Analysis and Applications》2004,296(1):340-350
The Cauchy problem of the homogeneous fractional-order evolution equation and evolutionary integral equation have been considered in [J. Fract. Calc. 7 (1995) 89] and [Korean J. Comput. Appl. Math. 9 (2002) 525]. The existence and uniqueness of the solution have been proved and the continuation of the solution and its fractional order derivative has been proved. Here we study the maximal regularity, continuation and some other properties of the Cauchy problem of the non-homogeneous fractional order evolution equation. 相似文献
15.
Under study is the Cauchy problem for the fractional diffusion equation with a Caputo derivative. The existence and uniqueness theorems for a smooth solution are proven in a weighted H¨older space. 相似文献
16.
Ya. I. Belopolskaya 《Journal of Mathematical Sciences》2006,133(3):1207-1223
We show in this paper that stochastic processes associated with nonlinear parabolic equations and systems allow one to construct
a probabilistic representation of a generalized solution to the Cauchy problem. We also show that in some cases the derived
representation can be used to construct a solution to the Cauchy problem for a hyperbolic system via the vanishing viscosity
method. Bibliography: 12 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 311, 2004, pp. 7–39. 相似文献
17.
In this paper, we are concerned with Cauchy problems of fractional differential equations with Riemann–Liouville fractional derivatives in infinite-dimensional Banach spaces. We introduce the notion of fractional resolvent, obtain some its properties, and present a generation theorem for exponentially bounded fractional resolvents. Moreover, we prove that a homogeneous α-order Cauchy problem is well posed if and only if its coefficient operator is the generator of an α-order fractional resolvent, and we give sufficient conditions to guarantee the existence and uniqueness of weak solutions and strong solutions of an inhomogeneous α-order Cauchy problem. 相似文献
18.
张思逸 《高校应用数学学报(A辑)》2021,36(1):83-88
研究了抽象空间中缓增分数阶微分方程解的吸引性.建立了Cauchy问题存在全局吸引解的充分条件.揭示了缓增分数阶导数求解分数微分方程解的特征. 相似文献
19.
In this paper we consider the Cauchy problem of the two-dimensional inviscid Bénard system with fractional diffusivity. We show that there is a global unique solution to this system with Yudovich?s type data. 相似文献
20.
A. V. Glushak 《Mathematical Notes》2005,77(1):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. 相似文献