共查询到20条相似文献,搜索用时 15 毫秒
1.
Ravi P. Agarwal Ghaus Ur Rahman Muhsina 《Mathematical Methods in the Applied Sciences》2023,46(2):2801-2839
In this article, we formulate fractional differential inclusion of pantograph type (IFDIP), incorporating impulsive behavior of the solution. The boundary conditions taken into account are nonlocal in nature. We will consider the convex problem and prove the Filippov–Wazewski-type theorem. Moreover, existence of solution, uniqueness of a solution, and the topological properties of the solution's set will be examined for the problem under consideration. In the second part, the study will be confined to the second-order impulsive fractional differential equation of pantograph type. For certain geometric characteristics of the solution's set, Aronszajn–Browder–Gupta-type results will be explored for the newly introduced differential equation. Also, it will prove the existence of solution for the first-order fractional differential equation of pantograph type having impulsive behavior of the solution. 相似文献
2.
In this work, a directed connection between the fractal structure and the fractional calculus has been achieved. The fractional space–time diffusion equation is derived using the comb-like structure as a background model. The solution of the obtained equation will be established for three different interesting cases. 相似文献
3.
We will prove the existence, uniqueness and regularity of the solution for a stochastic fractional partial differential equation driven by an additive fractional space–time white noise. Moreover, the absolute continuity of the solution is also obtained. 相似文献
4.
Ahmed M. A. El-Sayed Mohamed A. E. Aly 《Journal of Applied Mathematics and Computing》2002,9(2):525-533
The fractional order evolutionary integral equations have been considered by the first author in [6], the existence, uniqueness and some other properties of the solution have been proved. Here we study the continuation of the solution and its fractional order derivative. Also we study the generality of this problem and prove that the fractional order diffusion problem, the fractional order wave problem and the initial value problem of the equation of evolution are special cases of it. The abstract diffusion-wave problem will be given also as an application. 相似文献
5.
《Communications in Nonlinear Science & Numerical Simulation》2014,19(7):2220-2227
In this paper, the solution of the multi-order differential equations, by using Mellin transform, is proposed. It is shown that the problem related to the shift of the real part of the argument of the transformed function, arising when the Mellin integral operates on the fractional derivatives, may be overcame. Then, the solution may be found for any fractional differential equation involving multi-order fractional derivatives (or integrals). The solution is found in the Mellin domain, by solving a linear set of algebraic equations, whose inverse transform gives the solution of the fractional differential equation at hands. 相似文献
6.
周文学 《应用泛函分析学报》2011,13(4):405-412
应用Gteen函数将分数阶微分方程边值问题可转化为等价的积分方程.近来此方法被应用于讨论非线性分数阶微分方程边值问题解的存在性.讨论非线性分数阶微分方程边值问题,应用Green函数,将其转化为等价的积分方程,并设非线性项满足Caratheodory条件,利用非紧性测度的性质和M6nch’s不动点定理证明解的存在性. 相似文献
7.
Two‐dimensional shifted Legendre polynomial collocation method for electromagnetic waves in dielectric media via almost operational matrices
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Vijay Kumar Patel Somveer Singh Vineet Kumar Singh 《Mathematical Methods in the Applied Sciences》2017,40(10):3698-3717
In this paper, a numerical solution of fractional partial differential equations (FPDEs) for electromagnetic waves in dielectric media will be discussed. For the solution of FPDEs, we developed a numerical collocation method using an algorithm based on two‐dimensional shifted Legendre polynomials approximation, which is proposed for electromagnetic waves in dielectric media. By implementing the partial Riemann–Liouville fractional derivative operators, two‐dimensional shifted Legendre polynomials approximation and its operational matrix along with collocation method are used to convert FPDEs first into weakly singular fractional partial integro‐differential equations and then converted weakly singular fractional partial integro‐differential equations into system of algebraic equation. Some results concerning the convergence analysis and error analysis are obtained. Illustrative examples are included to demonstrate the validity and applicability of the technique. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
8.
We consider an initial-boundary value problem for a multidimensional fractional diffusion equation. The aim of the paper is to construct an integral transformation which establishes a biunique correspondence between the fractional diffusion equation and the hyperbolic one. This transformation can be used for proving the uniqueness of the solution of the inverse problem for the fractional diffusion equation. 相似文献
9.
By introducing the fractional derivatives in the sense of Caputo, we use the adomian decomposition method to construct the approximate solutions for the cubic nonlinear fractional Schordinger equation with time and space fractional derivatives. The exact solution of the cubic nonlinear Schrodinger equation is given as a special case of our approximate solution. This method is efficient and powerful in solving wide classes of nonlinear evolution fractional order equation. 相似文献
10.
11.
The Averaging Principle for Stochastic Fractional Partial Differential Equations with Fractional Noises
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The purpose of this paper is to establish an averaging principle for stochastic fractional partial differential equation of order α > 1 driven by a fractional noise.
We prove the existence and uniqueness of the global mild solution for the considered
equation by the fixed point principle. The solutions for SPDEs with fractional noises
can be approximated by the solution for the averaged stochastic systems in the sense
of p-moment under some suitable assumptions. 相似文献
12.
One builds the solution of GL equation in terms of the elliptic cn function of complex argument. The real part of the complex action,
, corresponds to the potential of a vortex lattice, and from here, through the elliptic function degeneration, to the vortex streets. Considering the vortex streets fixed on vacuum by a background magnetic field through pinning, from equating the current density to zero one determines the field structure: the mean value will be roughly equal to BC2, and its flux will be fractional. The fractional flux will be associated to quasi-particles obeying the ‘anyonic’ statistics. At low temperatures and high external magnetic field, the structure of background field will be of Cantorian type. 相似文献
13.
Safar Irandoust-Pakchin Somayeh Abdi-Mazraeh Ali Khani 《Computational Mathematics and Mathematical Physics》2017,57(12):2047-2056
In this paper, a variable-order fractional derivative nonlinear cable equation is considered. It is commonly accepted that fractional differential equations play an important role in the explanation of many physical phenomena. For this reason we need a reliable and efficient technique for the solution of fractional differential equations. This paper deals with the numerical solution of class of fractional partial differential equation with variable coefficient of fractional differential equation in various continues functions of spatial and time orders. Our main aim is to generalize the Chebyshev cardinal operational matrix to the fractional calculus. Finally, illustrative examples are included to demonstrate the validity and applicability of the presented technique. 相似文献
14.
In this paper, we focus on maximum principles of a time–space fractional diffusion equation. Maximum principles for classical solution and weak solution are all obtained by using properties of the time fractional derivative operator and the fractional Laplace operator. We deduce maximum principles for a full fractional diffusion equation, other than time-fractional and spatial-integer order diffusion equations. 相似文献
15.
The fundamental solution of the fractional diffusion equation of distributed order in time (usually adopted for modelling sub-diffusion processes) is obtained based on its Mellin–Barnes integral representation. Such solution is proved to be related via a Laplace-type integral to the Fox–Wright functions. A series expansion is also provided in order to point out the distribution of time-scales related to the distribution of the fractional orders. The results of the time fractional diffusion equation of a single order are also recalled and then re-obtained from the general theory. 相似文献
16.
《随机分析与应用》2013,31(5):1209-1233
Abstract In the paper we compute the explicit form of the fractional chaos decomposition of the solution of a fractional stochastic bilinear equation with the drift in the fractional chaos of order one and initial condition in a finite fractional chaos. The large deviations principle is also obtained for the one-dimensional distributions of the solution of the equation perturbed by a small noise. 相似文献
17.
This paper investigates the blow-up of solutions for a time fractional nonlinear reaction–diffusion equation with weakly spatial source. We first derive two sufficient conditions under which the solutions may blow up in finite time. Then, we prove the existence of global solution when the initial data are small enough. Moreover, the long time behavior of bounded solutions will be analyzed. 相似文献
18.
Extending the D’alembert solution to space–time Modified Riemann–Liouville fractional wave equations
Cresus F.L. Godinho J. Weberszpil J.A. Helayël-Neto 《Chaos, solitons, and fractals》2012,45(6):765-771
In the realm of complexity, it is argued that adequate modeling of TeV-physics demands an approach based on fractal operators and fractional calculus (FC). Non-local theories and memory effects are connected to complexity and the FC. The non-differentiable nature of the microscopic dynamics may be connected with time scales. Based on the Modified Riemann–Liouville definition of fractional derivatives, we have worked out explicit solutions to a fractional wave equation with suitable initial conditions to carefully understand the time evolution of classical fields with a fractional dynamics. First, by considering space–time partial fractional derivatives of the same order in time and space, a generalized fractional D’alembertian is introduced and by means of a transformation of variables to light-cone coordinates, an explicit analytical solution is obtained. To address the situation of different orders in the time and space derivatives, we adopt different approaches, as it will become clear throughout this paper. Aspects connected to Lorentz symmetry are analyzed in both approaches. 相似文献
19.
We develop a space-time fractional Schrödinger equation containing Caputo fractional derivative and the quantum Riesz fractional operator from a space fractional Schrödinger equation in this paper. By use of the new equation we study the time evolution behaviors of the space-time fractional quantum system in the time-independent potential fields and two cases that the order of the time fractional derivative is between zero and one and between one and two are discussed respectively. The space-time fractional Schrödinger equation with time-independent potentials is divided into a space equation and a time one. A general solution, which is composed of oscillatory terms and decay ones, is obtained. We investigate the time limits of the total probability and the energy levels of particles when time goes to infinity and find that the limit values not only depend on the order of the time derivative, but also on the sign (positive or negative) of the eigenvalues of the space equation. We also find that the limit value of the total probability can be greater or less than one, which means the space-time fractional Schrödinger equation describes the quantum system where the probability is not conservative and particles may be extracted from or absorbed by the potentials. Additionally, the non-Markovian time evolution laws of the space-time fractional quantum system are discussed. The formula of the time evolution of the mechanical quantities is derived and we prove that there is no conservative quantities in the space-time fractional quantum system. We also get a Mittag-Leffler type of time evolution operator of wave functions and then establish a Heisenberg equation containing fractional operators. 相似文献