A q-analog, also called a q-extension or q-generalization is a mathematical expression parameterized by a quantity q that generalized a known expression and reduces to the known expression in the limit . There are q-a...A q-analog, also called a q-extension or q-generalization is a mathematical expression parameterized by a quantity q that generalized a known expression and reduces to the known expression in the limit . There are q-analogs for the fractional, binomial coefficient, derivative, Integral, Fibonacci numbers and so on. In this paper, we give several results, some of them are new and others are generalizations of the main results of [1]. As well as we give a generalization to the key lemma ([2], lemma 1.3).展开更多
Several new q-integral inequalities are presented. Some of them are new, One concerning double integrals, and others are generalizations of results of Miao and Qi [1]. A new key lemma is proved as well.
The purpose of this paper is to establish some identities with products of qHermite polynomials, q-ultraspherical polynomials and reciprocals of q-binomial coefficients.
The aim of the present paper is to introduce and study a new type of q-Mellin transform [11], that will be called q-finite Mellin transform. In particular, we prove for this new transform an inversion formula and q-co...The aim of the present paper is to introduce and study a new type of q-Mellin transform [11], that will be called q-finite Mellin transform. In particular, we prove for this new transform an inversion formula and q-convolution product. The application of this transform is also earlier proposed in solving procedure for a new equation with a new fractional differential operator of a variational type.展开更多
In this paper, we present a procedure for the numerical q-calculation of the q-integrals based on appropriate nodes and weights which are determined such that the error of q-integration is mini-mized;a system of linea...In this paper, we present a procedure for the numerical q-calculation of the q-integrals based on appropriate nodes and weights which are determined such that the error of q-integration is mini-mized;a system of linear and nonlinear set of equations respectively are prepared to obtain the nodes and weights simultaneously;the error of q-integration is considered to be minimized under this condition;finally some application and numerical examples are given for comparison with the exact solution. At the end, the related tables of approximations are presented.展开更多
In this paper, we consider the fractional q-integral with variable lower limit of integration. We prove the semigroup property of these integrals, and a formula of Leibniz type. Finally, we evaluate fractional q-integ...In this paper, we consider the fractional q-integral with variable lower limit of integration. We prove the semigroup property of these integrals, and a formula of Leibniz type. Finally, we evaluate fractional q-integrals of some functions. The consideration of q-exponential function in that sense leads to q-analogs of Mittag-Leffier function.展开更多
文摘A q-analog, also called a q-extension or q-generalization is a mathematical expression parameterized by a quantity q that generalized a known expression and reduces to the known expression in the limit . There are q-analogs for the fractional, binomial coefficient, derivative, Integral, Fibonacci numbers and so on. In this paper, we give several results, some of them are new and others are generalizations of the main results of [1]. As well as we give a generalization to the key lemma ([2], lemma 1.3).
文摘Several new q-integral inequalities are presented. Some of them are new, One concerning double integrals, and others are generalizations of results of Miao and Qi [1]. A new key lemma is proved as well.
基金Supported by the National Natural Science Foundation of China（10771093） Supported by the Youth Foundation of Luoyang Normal College（2013-QNJJ-001） Supported by the Youth Foundation of the Luoyang Institute of Science and Technology（2012QZ05）
文摘The purpose of this paper is to establish some identities with products of qHermite polynomials, q-ultraspherical polynomials and reciprocals of q-binomial coefficients.
文摘The aim of the present paper is to introduce and study a new type of q-Mellin transform [11], that will be called q-finite Mellin transform. In particular, we prove for this new transform an inversion formula and q-convolution product. The application of this transform is also earlier proposed in solving procedure for a new equation with a new fractional differential operator of a variational type.
文摘In this paper, we present a procedure for the numerical q-calculation of the q-integrals based on appropriate nodes and weights which are determined such that the error of q-integration is mini-mized;a system of linear and nonlinear set of equations respectively are prepared to obtain the nodes and weights simultaneously;the error of q-integration is considered to be minimized under this condition;finally some application and numerical examples are given for comparison with the exact solution. At the end, the related tables of approximations are presented.
基金Supported by Ministry of Science,Technology and Development of Republic Serbia (Grant Nos.144023 and 144013)
文摘In this paper, we consider the fractional q-integral with variable lower limit of integration. We prove the semigroup property of these integrals, and a formula of Leibniz type. Finally, we evaluate fractional q-integrals of some functions. The consideration of q-exponential function in that sense leads to q-analogs of Mittag-Leffier function.
