scientific article; zbMATH DE number 1907576
From MaRDI portal
Publication:4805623
zbMath1056.44001MaRDI QIDQ4805623
Anatoliy Aleksandrovich Kilbas, Megumi Saigo
Publication date: 8 May 2003
Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Laplace transformStieltjes transformintegral transformsbibliographytextbook\(H\)-functionMeijer \(G\)-function\(G\)-transforms\(H\)-transformsBessel type integral transformspace \({\mathcal L}_{\nu,r}\)
Special integral transforms (Legendre, Hilbert, etc.) (44A15) Fractional derivatives and integrals (26A33) Laplace transform (44A10) Integral transforms of special functions (44A20) Generalized hypergeometric series, ({}_pF_q) (33C20) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Hypergeometric integrals and functions defined by them ((E), (G), (H) and (I) functions) (33C60) Research exposition (monographs, survey articles) pertaining to integral transforms (44-02)
Related Items
Asymptotic behaviours of solution to Caputo–Hadamard fractional partial differential equation with fractional Laplacian, Solution to the Fractional Order Euler-Poisson-Darboux Equation, Generalized diffusion and random search processes, On the characteristic function for Burr distributions, FRACTIONAL CALCULUS OPERATORS OF THE PRODUCT OF GENERALIZED MODIFIED BESSEL FUNCTION OF THE SECOND TYPE, On Meijer's G function Gm,np,p for m + n = p, Trace formulae for the heat-volume potential of the time-fractional heat equation, Об одном обобщении функции Бесселя, The role of the Fox-Wright functions in fractional sub-diffusion of distributed order, Multidimensional Time Fractional Diffusion Equation, Factorization of the fundamental solution to fractional Helmholtz equation, Integrability properties of integral transforms via Morrey spaces, Solvability of a Dirichlet problem for a time fractional diffusion-wave equation in Lipschitz domains, Identification of points sources via time fractional diffusion equation, Hypergeometric functions at unit argument: simple derivation of old and new identities, Регулярність розв'язків крайових задач для дифузійно-хвильового рівняння з узагальненими функціями в правих частинах, Study of results of Katugampola fractional derivative and Chebyshev inequailities, The Problem for a Mixed Equation with Fractional Power of the Bessel Operator, To the Properties of One Fox Function, Topological sensitivity analysis method in identifying of point sources via time-fractional diffusion equation, Fractional Schrödinger equation with Riesz-Feller derivative for delta potentials, Time-fractional telegraph equation with \(\psi\)-Hilfer derivatives, Limiting approach to generalized gamma Bessel model via fractional calculus and its applications in various disciplines, Gevrey type regularity of the Riesz-Feller operator perturbed by gradient in \(L^p(\mathbb{R})\), Solving the Euler-Poisson-Darboux equation of fractional order, Correlators of four light-ray operators in CCFT, Some families of the general Mathieu‐type series with associated properties and functional inequalities, Multi-dimensional integral transforms with the Fox \(H \)-function and the Legendre function of first kind in kernels on \(\mathfrak{L}_{\overline{\nu},\overline{r}} \)-spaces, Some results on the \({}_p R_q (\lambda,\mu; z)\) function involving pathway fractional integral operator and statistical distribution, Blowup for semilinear fractional diffusion system with Caputo–Hadamard derivative, Time-fractional telegraph equation of distributed order in higher dimensions with hilfer fractional derivatives, Cauchy problem for fractional advection-diffusion-asymmetry equations, Unnamed Item, Unnamed Item, Unnamed Item, Dirichlet boundary value problem in half-strip for fractional differential equation with Bessel operator and Riemann - Liouville partial derivative, An inverse fractional source problem in a space of periodic spatial distributions, Some new results related to a class of generalized Hurwitz zeta function, One-Dimensional and Multi-Dimensional Integral Transforms of Buschman–Erdélyi Type with Legendre Functions in Kernels, Unnamed Item, SOME PROPERTIES OF GENERALIZED BESSEL FUNCTION ASSOCIATED WITH GENERALIZED FRACTIONAL CALCULUS OPERATORS, Solution of fractional kinetic equation by a class of integral transform of pathway type, Scattering problems in the fractional quantum mechanics governed by the 2D space-fractional Schrödinger equation, Heat kernel for flat generalized Laplacians with anisotropic scaling, Unnamed Item, Unnamed Item, Некоторые новые обобщенные интегральные преобразования и их применение в теории дифференциальных уравнений, Задача Коши для уравнения параболического типа с оператором Бесселя и частной производной Римана-Лиувилля, Обобщeнное интегральное преобразование Лапласа и его применение к решению некоторых интегральных уравнений, The second boundary value problem in a half-strip for a B-parabolic equation with the Gerasimov–Caputo time derivative, An Integro-Differential Equation of the Fractional Form: Cauchy Problem and Solution, Об обобщeнной гипергеометрической функции Гаусса, Unnamed Item, ON A CLASS OF GENERALIZED FUNCTIONS FOR SOME INTEGRAL TRANSFORM ENFOLDING KERNELS OF MEIJER G FUNCTION TYPE, Existence and uniqueness of the solution for a time-fractional diffusion equation, Infinite wall in the fractional quantum mechanics, Distribution of products of independently distributed pathway random variables, Green's function for the time-dependent scattering problem in the fractional quantum mechanics, Restoration of the Initial Data in the Problem for a Diffusion Equation with Fractional Derivative with Respect to Time, On complete monotonicity of three parameter Mittag-Leffler function, The 𝑊^{𝑠,𝑝}-boundedness of stationary wave operators for the Schrödinger operator with inverse-square potential, Generalized fractional integral operators and the multivariable \(H\)-function, Some new facts concerning the delta neutral case of Fox's \(H\) function, New fractional calculus results involving Srivastava's general class of multivariable polynomials and the \(\overline{\mathrm{H}}\)-function, Representations and inequalities for generalized hypergeometric functions, A numerical scheme for the time-fractional diffusion equation by layer potentials, The Cauchy problem for the diffusion-wave equation with the Caputo partial derivative, Some results on the extended beta and extended hypergeometric functions, Hypergeometric differential equation and new identities for the coefficients of Nørlund and Bühring, Mellin transforms of generalized fractional integrals and derivatives, A new version of the generalized Krätzel-Fox integral operators, Existence conditions for a classical solution of the Cauchy problem for the diffusion-wave equation with a partial Caputo derivative, Some families of the incomplete \(H\)-functions and the incomplete \(\overline H \)-functions and associated integral transforms and operators of fractional calculus with applications, Extended Riemann-Liouville type fractional derivative operator with applications, First boundary-value problem in the half-strip for a parabolic-type equation with Bessel operator and Riemann-Liouville derivative, On some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation, Fundamental solutions of the time fractional diffusion-wave and parabolic Dirac operators, Decay estimates for time-fractional and other non-local in time subdiffusion equations in \(\mathbb R^d\), A certain class of Laplace transforms with applications to reaction and reaction-diffusion equations, Fractional reaction-diffusion equations, Reaction-diffusion systems and nonlinear waves, Solution of generalized fractional reaction-diffusion equations, Lie group symmetries as integral transforms of fundamental solutions, Historical survey: the chronicles of fractional calculus, Fractional integral operators characterized by some new hypergeometric summation formulas, Outage capacity evaluation of extended generalized-\(\mathcal K\) fading channel in the presence of random blockage, Unified approach to fractional calculus images involving the pathway transform of extended \(k\)-gamma function and applications, Time-fractional diffusion equation with \(\psi\)-Hilfer derivative, Fundamental solution of the multi-dimensional time fractional telegraph equation, Closed-form multi-dimensional solutions and asymptotic behaviors for subdiffusive processes with crossovers. I: Retarding case, Turán type inequalities for generalized Mittag-Leffler function, Functional inequalities for the Mittag-Leffler functions, On a generalized three-parameter Wright function of Le Roy type, Inversion of integral transform with an extended generalized Mittag-Leffler function, On a class of generalized Meijer-Laplace transforms of Fox function type kernels and their extension to a class of Boehmians, Extended Mittag-Leffler function and associated fractional calculus operators, On the fractional Poisson process and the discretized stable subordinator, On the parabolic Harnack inequality for non-local diffusion equations, A note on \(K_4\) fractional integral operator, On the spline collocation method for the single layer equation related to time-fractional diffusion, Further extended Caputo fractional derivative operator and its applications, Hypergeometric functions as generalized Stieltjes transforms, On properties of an entire function that is a generalization of the Wright function, Fractional-parabolic systems, On a class of space-time intrinsic random functions, Gamma distribution and extensions by using pathway idea, On fractional integration formulae for Aleph functions, Sequential fractional differential equations with Hadamard derivative, On the solutions of certain fractional kinetic equations, On some properties of the Mittag-Leffler function \(E_\alpha(-t^\alpha)\), completely monotone for \(t>0\) with \(0<\alpha<1\), On modifications of the gamma function by using Mittag-Leffler function, Fractional Green's function for the time-dependent scattering problem in the space-time-fractional quantum mechanics, Multihop Weibull-fading communications: performance analysis framework and applications, Exact distribution of the generalized Wilks's statistic and applications, Generalizations and applications of Srinivasa Ramanujan's integral associated with infinite Fourier sine transforms in terms of Meijer's \(G\)-function, Second boundary-value problem in a half-strip for equation of parabolic type with the Bessel operator and Riemann-liouvulle derivative, An inverse factorial series for a general gamma ratio and related properties of the Nørlund-Bernoulli polynomials, Subordination principle, Wright functions and large-time behavior for the discrete in time fractional diffusion equation, Representation of solutions and large-time behavior for fully nonlocal diffusion equations, Representations of hypergeometric functions for arbitrary parameter values and their use, Existence and uniqueness of the solution for a time-fractional diffusion equation with Robin boundary condition, A time-fractional Borel-Pompeiu formula and a related hypercomplex operator calculus, One inverse problem for the diffusion-wave equation in bounded domain, Mittag-Leffler functions and their applications, Fox \(H\) functions in fractional diffusion, Green's function for a pre-stressed thin plate on an elastic foundation under axisymmetric loading, On analogues of exponential functions for antisymmetric fractional derivatives, The Krätzel function and evaluation of integrals, A fractional generalization of the Dirichlet distribution and related distributions, Lamperti-type laws, The second boundary-value problem in a half-strip for a parabolic-type equation with Bessel operator and Riemann-Liouville partial derivative, Nonlinear stochastic time-fractional slow and fast diffusion equations on \(\mathbb{R}^d\), New integral representations for the Fox-Wright functions and its applications. II, An \(L_{q}(L_{p})\)-theory for the time-fractional evolution equations with variable coefficients, The Fox-Wright function near the singularity and the branch cut, Kubo fluctuation relations in the generalized elastic model, Anomalous diffusion with an irreversible linear reaction and sorption-desorption process, Conditions for the existence of a classical solution of a Cauchy type problem for the diffusion equation with a Riemann-Liouville partial derivative, Time-fractional telegraph equation of distributed order in higher dimensions, The blow-up and global existence of solution to Caputo-Hadamard fractional partial differential equation with fractional Laplacian, Fundamental solutions, transition densities and the integration of Lie symmetries, Certain fractional integral operators and the generalized multi-index Mittag-Leffler functions, A fast algorithm for fractional Helmholtz equation with application to electromagnetic waves propagation, On a fractional master equation, Certain inequalities for the modified Bessel-type function, Local well-posedness of semilinear space-time fractional Schrödinger equation, Some fractional calculus findings associated with the incomplete \(I\)-functions, An extension of the multiple Erdélyi-Kober operator and representations of the generalized hypergeometric functions, Some difference equations for Srivastava's \({\lambda}\)-generalized Hurwitz-Lerch zeta functions with applications, An extension of Wright function and its properties, A new representation for Srivastava's \(\lambda\)-generalized Hurwitz-Lerch zeta functions, Multi-dimensional generalized integral transform in the weighted spaces of summable functions, Multi-parametric Mittag-Leffler functions and their extension, The Mellin integral transform in fractional calculus, Science metrics on fractional calculus development since 1966, Reconfigurable intelligent surfaces-assisted terahertz communications, Fractional characteristic functions, and a fractional calculus approach for moments of random variables, Hölder regularity for the nonlinear stochastic time-fractional slow \& fast diffusion equations on \({\mathbb{R}}^d\), The Cauchy problem for an equation with fractional derivatives in Bessel potential spaces, Treatise on generalized Krätzel function, Completely monotonic gamma ratio and infinitely divisible H-function of Fox
