On the Dependence of Asymptotics of S-numbers of Fractional Integration Operators on Weight Functions
نویسنده
چکیده
We show that the singular values m of the fractional integration operator of order > 0 acting from weighted L 2 spaces of functions deened on the interval (?1; 1) or (0; 1) may, in both cases, have asymptotics m ? or m ?=2 , as m ! 1, depending on the speciic choice of weight functions. Some questions of singular value decompositions are also investigated for Riesz potential operators in weighted L 2 spaces of functions deened on R n .
منابع مشابه
On certain fractional calculus operators involving generalized Mittag-Leffler function
The object of this paper is to establish certain generalized fractional integration and differentiation involving generalized Mittag-Leffler function defined by Salim and Faraj [25]. The considered generalized fractional calculus operators contain the Appell's function $F_3$ [2, p.224] as kernel and are introduced by Saigo and Maeda [23]. The Marichev-Saigo-Maeda fractional calculus operators a...
متن کاملQuartic and pantic B-spline operational matrix of fractional integration
In this work, we proposed an effective method based on cubic and pantic B-spline scaling functions to solve partial differential equations of fractional order. Our method is based on dual functions of B-spline scaling functions. We derived the operational matrix of fractional integration of cubic and pantic B-spline scaling functions and used them to transform the mentioned equations to a syste...
متن کاملA Numerical Solution of Fractional Optimal Control Problems Using Spectral Method and Hybrid Functions
In this paper, a modern method is presented to solve a class of fractional optimal control problems (FOCPs) indirectly. First, the necessary optimality conditions for the FOCP are obtained in the form of two fractional differential equations (FDEs). Then, the unknown functions are approximated by the hybrid functions, including Bernoulli polynomials and Block-pulse functions based o...
متن کاملCertain subclass of $p$-valent meromorphic Bazilevi'{c} functions defined by fractional $q$-calculus operators
The aim of the present paper is to introduce and investigate a new subclass of Bazilevi'{c} functions in the punctured unit disk $mathcal{U}^*$ which have been described through using of the well-known fractional $q$-calculus operators, Hadamard product and a linear operator. In addition, we obtain some sufficient conditions for the func...
متن کاملHYBRID OF RATIONALIZED HAAR FUNCTIONS METHOD FOR SOLVING DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER
Abstract. In this paper, we implement numerical solution of differential equations of frac- tional order based on hybrid functions consisting of block-pulse function and rationalized Haar functions. For this purpose, the properties of hybrid of rationalized Haar functions are presented. In addition, the operational matrix of the fractional integration is obtained and is utilized to convert compu...
متن کامل