DSpace Collection: 2006
http://hdl.handle.net/10525/1244
The Collection's search engineSearch the Channelsearch
http://sci-gems.math.bas.bg/jspui/simple-search
Hankel Transform in Quantum Calculus and Applications
http://hdl.handle.net/10525/1289
Title: Hankel Transform in Quantum Calculus and Applications<br/><br/>Authors: Haddad, Meniar<br/><br/>Abstract: This paper is devoted to study the q-Hankel transform associated withthe third q-Bessel function called also Hahn-Exton function. We use the q-approximation of unit for establishing a q-inverse formula of this transform.Moreover, we establish the related q-Parseval theorem.<br/><br/>Description: Mathematics Subject Classification: 44A15, 33D15, 81Q99Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology
http://hdl.handle.net/10525/1288
Title: Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology<br/><br/>Authors: Andries, Erik; Umarov, Sabir; Steinberg, Stanly<br/><br/>Abstract: In this paper the multi-dimensional Monte-Carlo random walk simulation models governed by distributed fractional order differential equations(DODEs) and multi-term fractional order differential equations are constructed. The construction is based on the discretization leading to a generalized difference scheme (containing a finite number of terms in the timestep and infinite number of terms in the space step) of the Cauchy problemfor DODE. The scaling limits of the constructed random walks to a diffusionprocess in the sense of distributions is proved.<br/><br/>Description: Mathematics Subject Classification: 65C05, 60G50, 39A10, 92C37Numerical Approximation of a Fractional-In-Space Diffusion Equation (II) – with Nonhomogeneous Boundary Conditions
http://hdl.handle.net/10525/1287
Title: Numerical Approximation of a Fractional-In-Space Diffusion Equation (II) – with Nonhomogeneous Boundary Conditions<br/><br/>Authors: Ilic, M.; Liu, F.; Turner, I.; Anh, V.<br/><br/>Abstract: In this paper, a space fractional diffusion equation (SFDE) with nonhomogeneous boundary conditions on a bounded domain is considered. Anew matrix transfer technique (MTT) for solving the SFDE is proposed.The method is based on a matrix representation of the fractional-in-spaceoperator and the novelty of this approach is that a standard discretisationof the operator leads to a system of linear ODEs with the matrix raisedto the same fractional power. Analytic solutions of the SFDE are derived.Finally, some numerical results are given to demonstrate that the MTT isa computationally efficient and accurate method for solving SFDE.<br/><br/>Description: 2000 Mathematics Subject Classification: 26A33 (primary), 35S15Applications of the Owa-Srivastava Operator to the Class of K-Uniformly Convex Functions
http://hdl.handle.net/10525/1286
Title: Applications of the Owa-Srivastava Operator to the Class of K-Uniformly Convex Functions<br/><br/>Authors: Mishra, A. K.; Gochhayat, P.<br/><br/>Abstract: By making use of the fractional differential operator Ω^λz (0 ≤ λ < 1) dueto Owa and Srivastava, a new subclass of univalent functions denoted byk−SPλ (0 ≤ k < ∞) is introduced. The class k−SPλ unifies the concepts ofk-uniformly convex functions and k-starlike functions. Certain basic properties of k − SPλ such as inclusion theorem, subordination theorem, growththeorem and class preserving transforms are studied.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary 30C45, 26A33; Secondary 33C15On Maximal Function on the Laguerre Hypergroup
http://hdl.handle.net/10525/1285
Title: On Maximal Function on the Laguerre Hypergroup<br/><br/>Authors: Guliyev, Vagif; Assal, Miloud<br/><br/>Abstract: Let K = [0, ∞)×R be the Laguerre hypergroup which is the fundamentalmanifold of the radial function space for the Heisenberg group. In thispaper we consider the generalized shift operator, generated by Laguerrehypergroup, by means of which the maximal function is investigated. For1 < p ≤ ∞ the Lp(K)-boundedness and weak L1(K)-boundedness result forthe maximal function is obtained.<br/><br/>Description: 2000 Mathematics Subject Classification: 42B20, 42B25, 42B35Herz-Type Hardy Spaces for the Dunkl Operator on the Real Line
http://hdl.handle.net/10525/1284
Title: Herz-Type Hardy Spaces for the Dunkl Operator on the Real Line<br/><br/>Authors: Gasmi, A.; Sifi, M.; Soltani, F.<br/><br/>Abstract: We introduce some new weighted Herz spaces associated with the Dunkloperator on R. Also we characterize by atomic decompositions the corresponding Herz-type Hardy spaces. As applications we investigate the Dunkltransform on these spaces and establish a version of Hardy inequality forthis transform.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary 46F12, Secondary 44A15, 44A35q-Heat Operator and q-Poisson’s Operator
http://hdl.handle.net/10525/1283
Title: q-Heat Operator and q-Poisson’s Operator<br/><br/>Authors: Mabrouk, Hanène<br/><br/>Abstract: In this paper we study the q-heat and q-Poisson’s operators associatedwith the q-operator ∆q (see[5]). We begin by summarizing some statements concerning the q-even translation operator Tx,q, defined by Fitouhiand Bouzeffour in [5]. Then, we establish some basic properties of the q-heat semi-group such as boundedness and positivity. In the second part,we introduce the q-Poisson operator P^t, and address its main properties.We show in particular how these operators can be used to solve the initialand boundary value problems related to the q-heat and q-Laplace equationrespectively.<br/><br/>Description: 2000 Mathematics Subject Classification: 33D15, 33D90, 39A13An Analogue of Beurling-Hörmander’s Theorem for the Dunkl-Bessel Transform
http://hdl.handle.net/10525/1282
Title: An Analogue of Beurling-Hörmander’s Theorem for the Dunkl-Bessel Transform<br/><br/>Authors: Mejjaoli, Hatem<br/><br/>Abstract: We establish an analogue of Beurling-Hörmander’s theorem for the Dunkl-Bessel transform FD,B on R(d+1,+). We deduce an analogue of Gelfand-Shilov, Hardy, Cowling-Price and Morgan theorems on R(d+1,+) by using the heat kernel associated to the Dunkl-Bessel-Laplace operator.<br/><br/>Description: Mathematics Subject Classification: Primary 35R10, Secondary 44A15Generalized Sobolev Spaces of Exponential Type Associated with the Dunkl Operators
http://hdl.handle.net/10525/1281
Title: Generalized Sobolev Spaces of Exponential Type Associated with the Dunkl Operators<br/><br/>Authors: Assal, Miloud; Bouguila, Raouya<br/><br/>Abstract: In this paper we study generalized Sobolev spaces H^sG of exponentialtype associated with the Dunkl operators based on the space G of testfunctions for generalized hyperfunctions and investigate their properties.Moreover, we introduce a class of symbols of exponential type and their associated pseudodifferential operators related to the Dunkl operators, whichact naturally on H^sG.<br/><br/>Description: 2000 Mathematics Subject Classification: 35E45Mean-Periodic Functions Associated with the Jacobi-Dunkl Operator on R
http://hdl.handle.net/10525/1280
Title: Mean-Periodic Functions Associated with the Jacobi-Dunkl Operator on R<br/><br/>Authors: Ben Salem, N.; Ould Ahmed Salem, A.; Selmi, B.<br/><br/>Abstract: Using a convolution structure on the real line associated with the Jacobi-Dunkl differential-difference operator Λα,β given by: Λα,βf(x) = f'(x) + ((2α + 1) coth x + (2β + 1) tanh x) { ( f(x) − f(−x) ) / 2 }, α ≥ β ≥ −1/2, we define mean-periodic functions associated with Λα,β. We characterize these functions as an expansion series intervening appropriateelementary functions expressed in terms of the derivatives of the eigenfunction of Λα,β. Next, we deal with the Pompeiu type problem and convolution equations for this operator.<br/><br/>Description: 2000 Mathematics Subject Classification: 34K99, 44A15, 44A35, 42A75, 42A63Commutants of the Dunkl Operators in C(R)
http://hdl.handle.net/10525/1279
Title: Commutants of the Dunkl Operators in C(R)<br/><br/>Authors: Dimovski, Ivan; Hristov, Valentin; Sifi, Mohamed<br/><br/>Abstract: The Dunkl operators.<br/><br/>Description: 2000 Mathematics Subject Classification: 44A35; 42A75; 47A16, 47L10, 47L80On Integral Means for Fractional Calculus Operators of Multivalent Functions
http://hdl.handle.net/10525/1278
Title: On Integral Means for Fractional Calculus Operators of Multivalent Functions<br/><br/>Authors: Sümer Eker, S.; Özlem Güney, H.; Owa, Shigeyoshi<br/><br/>Abstract: Integral means inequalities are obtained for the fractional derivativesand the fractional integrals of multivalent functions. Relevant connectionswith various known integral means inequalities are also pointed out.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary 30C45, Secondary 26A33, 30C80On Two Saigo’s Fractional Integral Operators in the Class of Univalent Functions
http://hdl.handle.net/10525/1277
Title: On Two Saigo’s Fractional Integral Operators in the Class of Univalent Functions<br/><br/>Authors: Kiryakova, Virginia<br/><br/>Abstract: Recently, many papers in the theory of univalent functions have beendevoted to mapping and characterization properties of various linear integralor integro-differential operators in the class S (of normalized analytic andunivalent functions in the open unit disk U), and in its subclasses (as theclasses S∗ of the starlike functions and K of the convex functions in U).Among these operators, two operators introduced by Saigo, one involvingthe Gauss hypergeometric function, and the other - the Appell (or Horn)F3-function, are rather popular. Here we view on these Saigo’s operatorsas cases of generalized fractional integration operators, and show that thetechniques of the generalized fractional calculus and special functions arehelpful to obtain explicit sufficient conditions that guarantee mappings as:S → S and K → S, that is, preserving the univalency of functions.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary 26A33, 30C45; Secondary 33A35Some Mean-Value Theorems of the Cauchy Type
http://hdl.handle.net/10525/1276
Title: Some Mean-Value Theorems of the Cauchy Type<br/><br/>Authors: Pecaric, Josip; Rodic Lipanovic, Mirna; Srivastava, H. M.<br/><br/>Abstract: Some mean-value theorems of the Cauchy type, which are connectedwith Jensen’s inequality, are given in [2] in discrete form and in [5] in integralform. Several further generalizations and applications of these results arepresented here.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary 26A24, 26D15; Secondary 41A05Krätzel Function as a Function of Hypergeometric Type
http://hdl.handle.net/10525/1275
Title: Krätzel Function as a Function of Hypergeometric Type<br/><br/>Authors: Kilbas, Anatoly; Saxena, R. K.; Trujillo, Juan<br/><br/>Abstract: The paper is devoted to the study of the function Zνρ(x) defined forpositive x > 0, real ρ ∈ R and complex ν ∈ C, being such that Re(ν) < 0for ρ ≤ 0, [...]Such a function was earlier investigated for ρ > 0. Using the Mellin transform of Zνρ(x), we establish its representations in terms of the H-functionand extend this function from positive x > 0 to complex z. The resultsobtained, being different for ρ > 0 and ρ < 0, are applied to obtain the explicit forms of Zνρ(z) in terms of the generalized Wright function. The cases,when such representations are expressed via the generalized hypergeometricfunctions, are given.<br/><br/>Description: 2000 Mathematics Subject Classification: 33C60, 33C20, 44A15On the Generalized Confluent Hypergeometric Function and Its Application
http://hdl.handle.net/10525/1274
Title: On the Generalized Confluent Hypergeometric Function and Its Application<br/><br/>Authors: Virchenko, Nina<br/><br/>Abstract: This paper is devoted to further development of important case ofWright’s hypergeometric function and its applications to the generalizationof Γ-, B-, ψ-, ζ-, Volterra functions.<br/><br/>Description: 2000 Mathematics Subject Classification: 26A33, 33C20