DSpace Collection: 2005
http://hdl.handle.net/10525/1226
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Fractional Extensions of Jacobi Polynomials and Gauss Hypergeometric Function
http://hdl.handle.net/10525/1267
Title: Fractional Extensions of Jacobi Polynomials and Gauss Hypergeometric Function<br/><br/>Authors: Gogovcheva, Elena; Boyadjiev, Lyubomir<br/><br/>Abstract: This paper refers to a fractional order generalization of the classical Jacobi polynomials. Rodrigues’ type representation formula of fractional orderis considered. By means of the Riemann–Liouville operator of fractional calculus fractional Jacobi functions are defined, some of their properties aregiven and compared with the corresponding properties of the classical Jacobi polynomials. These functions appear as a special case of a fractionalGauss function, defined as a solution of the fractional generalization of theGauss hypergeometric equation.<br/><br/>Description: 2000 Mathematics Subject Classification: 26A33, 33C45Cauchy-Type Problem for Diffusion-Wave Equation with the Riemann-Liouville Partial Derivative
http://hdl.handle.net/10525/1266
Title: Cauchy-Type Problem for Diffusion-Wave Equation with the Riemann-Liouville Partial Derivative<br/><br/>Authors: Kilbas, Anatoly; Trujillo, Juan; Voroshilov, Aleksandr<br/><br/>Abstract: The paper is devoted to the study of the Cauchy-type problem for thedifferential equation [...] involving the Riemann-Liouville partial fractional derivative of order α > 0 [...] and the Laplace operator.<br/><br/>Description: 2000 Mathematics Subject Classification: 35A15, 44A15, 26A33On Multidimensional Analogue of Marchaud Formula for Fractional Riesz-Type Derivatives in Domains in R^n
http://hdl.handle.net/10525/1265
Title: On Multidimensional Analogue of Marchaud Formula for Fractional Riesz-Type Derivatives in Domains in R^n<br/><br/>Authors: Rafeiro, Humberto; Samko, Stefan<br/><br/>Abstract: There is given a generalization of the Marchaud formula for one-dimensional fractional derivatives on an interval (a, b), −∞ < a < b ≤ ∞, to themultidimensional case of functions defined on a region in R^n<br/><br/>Description: 2000 Mathematics Subject Classification: 26A33, 42B20Inhomogeneous Fractional Diffusion Equations
http://hdl.handle.net/10525/1264
Title: Inhomogeneous Fractional Diffusion Equations<br/><br/>Authors: Baeumer, Boris; Kurita, Satoko; Meerschaert, Mark<br/><br/>Abstract: Fractional diffusion equations are abstract partial differential equationsthat involve fractional derivatives in space and time. They are useful tomodel anomalous diffusion, where a plume of particles spreads in a differentmanner than the classical diffusion equation predicts. An initial value problem involving a space-fractional diffusion equation is an abstract Cauchyproblem, whose analytic solution can be written in terms of the semigroupwhose generator gives the space-fractional derivative operator. The corresponding time-fractional initial value problem is called a fractional Cauchyproblem. Recently, it was shown that the solution of a fractional Cauchyproblem can be expressed as an integral transform of the solution to thecorresponding Cauchy problem. In this paper, we extend that results toinhomogeneous fractional diffusion equations, in which a forcing functionis included to model sources and sinks. Existence and uniqueness is established by considering an equivalent (non-local) integral equation. Finally,we illustrate the practical application of these results with an example fromgroundwater hydrology, to show the effect of the fractional time derivativeon plume evolution, and the proper specification of a forcing function in atime-fractional evolution equation.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary 26A33; Secondary 35S10, 86A05Convolution Products in L1(R+), Integral Transforms and Fractional Calculus
http://hdl.handle.net/10525/1263
Title: Convolution Products in L1(R+), Integral Transforms and Fractional Calculus<br/><br/>Authors: Miana, Pedro<br/><br/>Abstract: We prove equalities in the Banach algebra L1(R+). We apply them to integral transforms and fractional calculus.<br/><br/>Description: Mathematics Subject Classification: 43A20, 26A33 (main), 44A10, 44A15An Abstract Second Kind Fredholm Integral Equation with Degenerated Kernel
http://hdl.handle.net/10525/1262
Title: An Abstract Second Kind Fredholm Integral Equation with Degenerated Kernel<br/><br/>Authors: Wysocki, Hubert; Zellma, Marek<br/><br/>Abstract: The paper presents an abstract linear second kind Fredholm integral equation with degenerated kernel defined by means of the Bittner operational calculus. Fredholm alternative for mutually conjugated integral equations is also shown here. Some examples of solutions of the considered integral equation in various operational calculus models are also given.<br/><br/>Description: Mathematics Subject Classification: 44A40, 45B05Numerical Approximation of a Fractional-In-Space Diffusion Equation, I
http://hdl.handle.net/10525/1261
Title: Numerical Approximation of a Fractional-In-Space Diffusion Equation, I<br/><br/>Authors: Ilic, M.; Liu, F.; Turner, I.; Anh, V.<br/><br/>Abstract: This paper provides a new method and corresponding numerical schemesto approximate a fractional-in-space diffusion equation on a bounded domain under boundary conditions of the Dirichlet, Neumann or Robin type.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. Numerical results are provided to gauge theperformance of the proposed method relative to exact analytical solutionsdetermined using a spectral representation of the fractional derivative. Initial results for a variety of one-dimensional test problems appear promising.Furthermore, the proposed strategy can be generalised to higher dimensions.<br/><br/>Description: 2000 Mathematics Subject Classification: 26A33 (primary), 35S15 (secondary)On the Riemann-Liouville Fractional q-Integral Operator Involving a Basic Analogue of Fox H-Function
http://hdl.handle.net/10525/1260
Title: On the Riemann-Liouville Fractional q-Integral Operator Involving a Basic Analogue of Fox H-Function<br/><br/>Authors: Kalla, S.; Yadav, R.; Purohit, S.<br/><br/>Abstract: The present paper envisages the applications of Riemann-Liouville fractional q-integral operator to a basic analogue of Fox H-function. Results involving the basic hypergeometric functions like Gq(.), Jv(x; q), Yv(x; q),Kv(x; q), Hv(x; q) and various other q-elementary functions associated with the Riemann-Liouville fractional q-integral operator have been deduced as special cases of the main result.<br/><br/>Description: 2000 Mathematics Subject Classification: 33D60, 26A33, 33C60An Lp − Lq - Version of Morgan's Theorem Associated with Partial Differential Operators
http://hdl.handle.net/10525/1259
Title: An Lp − Lq - Version of Morgan's Theorem Associated with Partial Differential Operators<br/><br/>Authors: Kamoun, Lotfi<br/><br/>Abstract: In this paper we take the strip KL = [0, +∞[×[−Lπ, Lπ], where L is apositive integer. We consider, for a nonnegative real number α, two partialdifferential operators D and Dα on ]0, +∞[×] − Lπ, Lπ[. We associate ageneralized Fourier transform Fα to the operators D and Dα. For this transform Fα, we establish an Lp − Lq − version of the Morgan's theorem under the assumption 1 ≤ p, q ≤ +∞.<br/><br/>Description: 2000 Mathematics Subject Classification: 42B10, 43A32.Asymptotic Property of Eigenvalues and Eigenfunctions of the Laplace Operator in Domain with a Perturbed Boundary
http://hdl.handle.net/10525/1258
Title: Asymptotic Property of Eigenvalues and Eigenfunctions of the Laplace Operator in Domain with a Perturbed Boundary<br/><br/>Authors: Khelifi, Abdessatar<br/><br/>Abstract: In this paper, we consider the variations of eigenvalues and eigenfunctions for the Laplace operator with homogeneous Dirichlet boundary conditions under deformation of the underlying domain of definition. We deriverecursive formulas for the Taylor coefficients of the eigenvalues as functionsof the shape-perturbation parameter and we establish the existence of a setof eigenfunctions that is jointly holomorphic in the spatial and boundary-variation variables. Using integral equations, we show that these eigenvalues are exactly built with the characteristic values of some meromorphicoperator-valued functions.<br/><br/>Description: 2000 Mathematics Subject Classification: 35J05, 35C15, 44P05Generalization of the Modified Bessel Function and Its Generating Function
http://hdl.handle.net/10525/1257
Title: Generalization of the Modified Bessel Function and Its Generating Function<br/><br/>Authors: Griffiths, J.; Leonenko, G.; Williams, J.<br/><br/>Abstract: This paper presents new generalizations of the modified Bessel functionand its generating function. This function has important application in thetransient solution of a queueing system.<br/><br/>Description: 2000 Mathematics Subject Classification: 33C10, 33-02, 60K25On a Singular Value Problem for the Fractional Laplacian on the Exterior of the Unit Ball
http://hdl.handle.net/10525/1256
Title: On a Singular Value Problem for the Fractional Laplacian on the Exterior of the Unit Ball<br/><br/>Authors: Bezzarga, Mounir; Kefi, Khaled<br/><br/>Abstract: We study a singular value problem and the boundary Harnack principlefor the fractional Laplacian on the exterior of the unit ball.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary 26A33; Secondary47G20, 31B05Rough Maximal Oscillatory Singular Integral Operators
http://hdl.handle.net/10525/1255
Title: Rough Maximal Oscillatory Singular Integral Operators<br/><br/>Authors: Al-Salman, Ahmad<br/><br/>Abstract: In this paper, we establish the L^p boundedness of certain maximal oscillatory singular integral operators with rough kernels belonging to certain block spaces. Our L^p boundedness result improves previously known results.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary 42B20; Secondary 42B15, 42B25Fractional Powers of Almost Non-Negative Operators
http://hdl.handle.net/10525/1254
Title: Fractional Powers of Almost Non-Negative Operators<br/><br/>Authors: Martínez, Celso; Sanz, Miguel; Redondo, Antonia<br/><br/>Abstract: In this paper, we extend the theory of complex powers of operators to aclass of operators in Banach spaces whose spectrum lies in C \ ]−∞, 0[ andwhose resolvent satisfies an estimate ||(λ + A)^(−1)|| ≤ (λ^(−1) + λ^m)M for all λ > 0 and for some constants M > 0 and m ∈ R. This class of operatorsstrictly contains the class of the non negative operators and the one ofoperators with polynomially bounded resolvent. We also prove that thistheory may be extended to sequentially complete locally convex spaces.<br/><br/>Description: Mathematics Subject Classification: Primary 47A60, 47D06.Discrete Models of Time-Fractional Diffusion in a Potential Well
http://hdl.handle.net/10525/1253
Title: Discrete Models of Time-Fractional Diffusion in a Potential Well<br/><br/>Authors: Gorenflo, R.; Abdel-Rehim, E.<br/><br/>Abstract: By generalization of Ehrenfest’s urn model, we obtain discrete approximations to spatially one-dimensional time-fractional diffusion processes withdrift towards the origin. These discrete approximations can be interpreted(a) as difference schemes for the relevant time-fractional partial differentialequation, (b) as random walk models. The relevant convergence questions aswell as the behaviour for time tending to infinity are discussed, and resultsof numerical case studies are displayed.See also, http://www.diss.fu-berlin.de/2004/168/index.html<br/><br/>Description: Mathematics Subject Classification: 26A33, 45K05, 60J60, 60G50, 65N06, 80-99.LP → LQ - Estimates for the Fractional Acoustic Potentials and some Related Operators
http://hdl.handle.net/10525/1252
Title: LP → LQ - Estimates for the Fractional Acoustic Potentials and some Related Operators<br/><br/>Authors: Karapetyants, Alexey; Karasev, Denis; Nogin, Vladimir<br/><br/>Abstract: We obtain the Lp → Lq - estimates for the fractional acoustic potentials in R^n, which are known to be negative powers of the Helmholtz operator, and some related operators. Some applications of these estimates are also given.<br/><br/>Description: Mathematics Subject Classification: 47B38, 31B10, 42B20, 42B15.