Related papers: Splines and Fractional Differential Operators
We prove some existence results for a class of nonlinear fractional equations driven by a nonlocal operator.
Differential operators usually result in derivatives expressed as a ratio of differentials. For all but the simplest derivatives, these ratios are typically not algebraically manipulable, but must be held together as a unit in order to…
In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…
Fractional difference sequence spaces have been studied in the literature recently. In this work, some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain operators on some difference…
We study arbitrary order symmetry operators for the linear Schr\"odinger equations with arbitrary number of spatial variables. We deduce determining equations for coefficient functions of such operators and consider in detail some cases…
This paper is devoted to the question of constructing a higher order Faber spline basis for the sampling discretization of functions with higher regularity than Lipschitz. The basis constructed in this paper has similar properties as the…
In this paper Quintic Spline is defined for the numerical solutions of the fourth order linear special case Boundary Value Problems. End conditions are also derived to complete the definition of spline.The algorithm developed approximates…
We show that any differential operator of the form $L(y)=\sum_{k=0}^{k=N} a_{k}(x) y^{(k)}$, where $a_k$ is a real polynomial of degree $\leq k$, has all real eigenvalues in the space of polynomials of degree at most n, for all n. The…
In this letter we are concerned with the possibility to approach the existence of solutions to a class of discontinuous dynamical systems of fractional order. In this purpose, the underlying initial value problem is transformed into a…
In this study, depending on the upper and the lower indices of the hyperharmonic number $h_{n}^{(r)}$, nonlinear recurrence relations are obtained. It is shown that generalized harmonic number and hyperharmonic number can be obtained from…
Based on an original classification of differential equations by types of regular Lie group actions, we offer a systematic procedure for describing partial differential equations with prescribed symmetry groups. Using a new powerful…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
A symmetric function of $N$ variables can be given in terms of symmetric polynomials of these variables. We determine those symmetric polynomials in which the dual differential operators take the neatest form when expressed in terms of our…
We provide the solution to the normal ordering problem for powers and exponentials of two classes of operators. The first one consists of boson strings and more generally homogeneous polynomials, while the second one treats operators linear…
The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the…
We study integrable hierarchies associated with spectral problems of the form $P\psi=\lambda Q\psi$ where $P,Q$ are difference operators. The corresponding nonlinear differential-difference equations can be viewed as inhomogeneous…
We present an approach how to obtain solutions of arbitrary linear operator equation for unknown functions. The particular solution can be represented by the infinite operator series (Cyclic Operator Decomposition), which acts the…
We define a class of discrete operators that, in particular, include the delta and nabla fractional operators.
The method of constructing spline classes in the form of trigonometric Fourier series whose coefficients have a certain decreasing order are considered. in turn, this decrement determines the number of continuous derivatives of sum of this…
This work concerns stationary Stokes type systems governed by a general class of non-necessarily power-type nonlinearities. Fractional regularity properties of the symmetric gradient of local solutions are established, depending on a…