DSpace Collection: 2004
http://hdl.handle.net/10525/1225
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From Differences to Derivatives
http://hdl.handle.net/10525/1238
Title: From Differences to Derivatives<br/><br/>Authors: Duarte Ortigueira, Manuel; Coito, Fernando<br/><br/>Abstract: A relation showing that the Grünwald-Letnikov and generalized Cauchyderivatives are equal is deduced confirming the validity of a well knownconjecture. Integral representations for both direct and reverse fractionaldifferences are presented. From these the fractional derivative is readilyobtained generalizing the Cauchy integral formula.Thu, 01 Jan 2004 00:00:00 GMTWeighted Theorems on Fractional Integrals in the Generalized Hölder Spaces via Indices mω and Mω
http://hdl.handle.net/10525/1237
Title: Weighted Theorems on Fractional Integrals in the Generalized Hölder Spaces via Indices mω and Mω<br/><br/>Authors: Karapetyants, Nikolai; Samko, Natasha<br/><br/>Abstract: There are known various statements on weighted action of one-dimensional and multidimensional fractional integration operators in spaces of continuous functions, such as weighted generalized Hölder spaces Hω0(ρ) of functions with a given dominant ω of their continuity modulus.<br/><br/>Description: Mathematics Subject Classification: 26A16, 26A33, 46E15.Thu, 01 Jan 2004 00:00:00 GMTGeneralized Strichartz Inequalities for the Wave Equation on the Laguerre Hypergroup
http://hdl.handle.net/10525/1236
Title: Generalized Strichartz Inequalities for the Wave Equation on the Laguerre Hypergroup<br/><br/>Authors: Assal, Miloud; Ben Abdallah, Hacen<br/><br/>Abstract: In this paper we study generalized Strichartz inequalities for the waveequation on the Laguerre hypergroup using generalized homogeneous Besov-Laguerre type spaces.<br/><br/>Description: Mathematics Subject Classification: 42B35, 35L35, 35K35Thu, 01 Jan 2004 00:00:00 GMTOn the Mellin Transforms of Dirac’S Delta Function, The Hausdorff Dimension Function, and The Theorem by Mellin
http://hdl.handle.net/10525/1235
Title: On the Mellin Transforms of Dirac’S Delta Function, The Hausdorff Dimension Function, and The Theorem by Mellin<br/><br/>Authors: Südland, Norbert; Baumann, Gerd<br/><br/>Abstract: We prove that Dirac’s (symmetrical) delta function and the Hausdorffdimension function build up a pair of reciprocal functions. Our reasoningis based on the theorem by Mellin. Applications of the reciprocity relationdemonstrate the merit of this approach.<br/><br/>Description: Mathematics Subject Classification: 44A05, 46F12, 28A78Thu, 01 Jan 2004 00:00:00 GMTSuggestion from the Past?
http://hdl.handle.net/10525/1234
Title: Suggestion from the Past?<br/><br/>Authors: Machado, J.; Jesus, Isabel<br/><br/>Abstract: The generalization of the concept of derivative to non-integer values goesback to the beginning of the theory of differential calculus. Nevertheless, itsapplication in physics and engineering remained unexplored up to the lasttwo decades. Recent research motivated the establishment of strategies taking advantage of the Fractional Calculus (FC) in the modeling and controlof many phenomena. In fact, many classical engineering applications deserve a closer attention and a new analysis in the viewpoint of FC. Bearingthese ideas in mind, this work addresses the partial differential equationsthat model the electrical transmission lines. The distributed characteristicsof this system may lead to design techniques, for integrated circuits, capableof implementing directly fractional-order impedances and, therefore, constitutes an alternative to exploring fractal geometries and dielectric properties.<br/><br/>Description: Mathematics Subject Classification: 26A33 (main), 35A22, 78A25, 93A30Thu, 01 Jan 2004 00:00:00 GMTOn the Range of the Fourier Transform Associated with the Spherical Mean Operator
http://hdl.handle.net/10525/1233
Title: On the Range of the Fourier Transform Associated with the Spherical Mean Operator<br/><br/>Authors: Jelassi, M.; Rachdi, L.<br/><br/>Abstract: We characterize the range of some spaces of functions by the Fouriertransform associated with the spherical mean operator R and we give anew description of the Schwartz spaces. Next, we prove a Paley-Wiener anda Paley-Wiener-Schawrtz theorems.Thu, 01 Jan 2004 00:00:00 GMTAn Expansion Formula for Fractional Derivatives and its Application
http://hdl.handle.net/10525/1232
Title: An Expansion Formula for Fractional Derivatives and its Application<br/><br/>Authors: Atanackovic, T.; Stankovic, B.<br/><br/>Abstract: An expansion formula for fractional derivatives given as in form of aseries involving function and moments of its k-th derivative is derived. Theconvergence of the series is proved and an estimate of the reminder is given.The form of the fractional derivative given here is especially suitable inderiving restrictions, in a form of internal variable theory, following fromthe second law of thermodynamics, when applied to linear viscoelasticity offractional derivative type.Thu, 01 Jan 2004 00:00:00 GMTOperational Rules for a Mixed Operator of the Erdélyi-Kober Type
http://hdl.handle.net/10525/1231
Title: Operational Rules for a Mixed Operator of the Erdélyi-Kober Type<br/><br/>Authors: Luchko, Yury<br/><br/>Abstract: In the paper, the machinery of the Mellin integral transform is appliedto deduce and prove some operational relations for a general operator of theErdélyi-Kober type. This integro-differential operator is a composition ofa number of left-hand sided and right-hand sided Erdélyi-Kober derivativesand integrals. It is referred to in the paper as a mixed operator of theErdélyi-Kober type.For special values of parameters, the operator is reduced to some wellknown differential, integro-differential, or integral operators studied earlierby different authors. The differential operators of hyper-Bessel type, theRiemann-Liouville fractional derivative, the Caputo fractional derivative,and the multiple Erdélyi-Kober fractional derivatives and integrals are examples of its particular cases. In the general case however, the constructionssuggested in the paper are new objects not yet well studied in the literature. The initial impulse to consider the operators presented in the paperarose while the author studied a problem to find scale-invariant solutions ofsome partial differential equations of fractional order: It turned out, thatscale-invariant solutions of these partial differential equations of fractionalorder are described by ordinary differential equations of fractional ordercontaining some particular cases of the mixed operator of Erdélyi-Kobertype.<br/><br/>Description: 2000 Mathematics Subject Classification: 26A33 (main), 44A40, 44A35, 33E30, 45J05, 45D05Thu, 01 Jan 2004 00:00:00 GMTA Generalized Convolution with a Weight Function for the Fourier Cosine and Sine Transforms
http://hdl.handle.net/10525/1230
Title: A Generalized Convolution with a Weight Function for the Fourier Cosine and Sine Transforms<br/><br/>Authors: Xuan Thao, Nguyen; Kim Tuan, Vu; Minh Khoa, Nguyen<br/><br/>Abstract: A generalized convolution with a weight function for the Fourier cosineand sine transforms is introduced. Its properties and applications to solvinga system of integral equations are considered.Thu, 01 Jan 2004 00:00:00 GMTCauchy Problem for Differential Equation with Caputo Derivative
http://hdl.handle.net/10525/1229
Title: Cauchy Problem for Differential Equation with Caputo Derivative<br/><br/>Authors: Kilbas, Anatoly; Marzan, Sergei<br/><br/>Abstract: The paper is devoted to the study of the Cauchy problem for a nonlineardifferential equation of complex order with the Caputo fractional derivative.The equivalence of this problem and a nonlinear Volterra integral equationin the space of continuously differentiable functions is established. On thebasis of this result, the existence and uniqueness of the solution of theconsidered Cauchy problem is proved. The approximate-iterative methodby Dzjadyk is used to obtain the approximate solution of this problem. Twonumerical examples are given.Thu, 01 Jan 2004 00:00:00 GMTPowers and Logarithms
http://hdl.handle.net/10525/1228
Title: Powers and Logarithms<br/><br/>Authors: Przeworska-Rolewicz, Danuta<br/><br/>Abstract: There are applied power mappings in algebras with logarithms inducedby a given linear operator D in order to study particular properties of powersof logarithms. Main results of this paper will be concerned with the casewhen an algebra under consideration is commutative and has a unit andthe operator D satisfies the Leibniz condition, i.e. D(xy) = xDy + yDx forx, y ∈ dom D. Note that in the Number Theory there are well-known severalformulae expressed by means of some combinations of powers of logarithmicand antilogarithmic mappings or powers of logarithms and antilogarithms(cf. for instance, the survey of Schinzel S[1].Thu, 01 Jan 2004 00:00:00 GMTOn some Mixture Distributions
http://hdl.handle.net/10525/1227
Title: On some Mixture Distributions<br/><br/>Authors: Nakhi, Y. Ben; Kalla, S.L.<br/><br/>Abstract: The aim of this paper is to establish some mixture distributions that arise in stochastic processes. Some basic functions associated with the probability mass function of the mixture distributions, such as k-th moments, characteristic function and factorial moments are computed. Further we obtain a three-term recurrence relation for each established mixture distribution.Thu, 01 Jan 2004 00:00:00 GMT