scientific article; zbMATH DE number 615020

Publication date: 8 August 1994

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

monograph integral equations inversion convolutions operational calculus fractional integral operators Mellin transformation Kontorovich-Lebedev transformation Leibniz rules Parseval theorem \(G\)-function kernels hypergeometric functions as kernels index transformations \(H\)-function kernels rings and fields of operators

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Fractional derivatives and integrals (26A33) Calculus of Mikusi?ski and other operational calculi (44A40) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Hypergeometric integrals and functions defined by them ((E), (G), (H) and (I) functions) (33C60) Integral equations with miscellaneous special kernels (45H05) Research exposition (monographs, survey articles) pertaining to integral transforms (44-02)

Related Items (only showing first 100 items - show all)

On a variant of multivariate Mittag-Leffler's function arising in the Laplace transform method ⋮ Generalization of Titchmarsh's theorem for the modified Whittaker transform ⋮ On the theory of orthogonal polynomials for the weight xνexp(−x−t/x). II ⋮ Nonlinear Riemann-Liouville fractional differential equations with nonlocal Erdélyi-Kober fractional integral conditions ⋮ Existence of solutions for Riemann-Liouville fractional differential equations with nonlocal Erdélyi-Kober integral boundary conditions on the half-line ⋮ Mikusiński's operational calculus for Prabhakar fractional calculus ⋮ On the Weber type integral equation related to the Weber-Titchmarsh problem ⋮ Mellin transforms of generalized fractional integrals and derivatives ⋮ Fractional integration operator on some radial rays and intertwining for the Dunkl operator ⋮ On the product formula and convolution associated with the index Whittaker transform ⋮ System of fractional differential equations with Erdélyi-Kober fractional integral conditions ⋮ Fundamental solutions for the two dimensional affine group and \(\mathbb{H}^{n + 1}\) ⋮ Discrete Fourier-Jacobi transform ⋮ Analytical solution of the generalized space-time fractional ultra-hyperbolic differential equation ⋮ Lebedev–Skalskaya transforms and allied operators on certain function spaces ⋮ Differential and integral relations in the class of multi-index Mittag-Leffler functions ⋮ On some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation ⋮ Reverse convolution inequalities for Lebedev-Skalskaya transforms ⋮ Fourier type transforms on Lie symmetry groups ⋮ On Especial Cases of Boas-Buck-Type Polynomial Sequences ⋮ Whittaker-Stockwell transform and Tikhonov regularization problem ⋮ Historical survey: the chronicles of fractional calculus ⋮ Fock-type spaces associated to higher-order Bessel operator ⋮ The Mehler-Fock-Clifford transform and pseudo-differential operator on function spaces ⋮ Orthogonal polynomials with ultra-exponential weight functions: an explicit solution to the Ditkin-Prudnikov problem ⋮ A method of composition orthogonality and new sequences of orthogonal polynomials and functions for non-classical weights ⋮ The Hermite functions related to infinite series of generalized convolutions and applications ⋮ New classes of non-convolution integral equations arising from Lie symmetry analysis of hyperbolic pdes ⋮ Operational method for solving fractional differential equations with the left-and right-hand sided Erdélyi-Kober fractional derivatives ⋮ Fractional calculus operators of special functions? The result is well predictable! ⋮ A modification of the Prudnikov and Laguerre polynomials ⋮ An operational approach with application to fractional Bessel equation ⋮ Product of pseudo-differential operators associated with zero order Mehler-Fock transform ⋮ New cases of Hankel operator diagonalization ⋮ On the theory of orthogonal polynomials for the weight x^ν exp (−x − t/x). I ⋮ On the Weber integral equation and solution to the Weber-Titchmarsh problem ⋮ Applications of generalized convolutions associated with the Fourier and Hartley transforms ⋮ An operational calculus formulation of fractional calculus with general analytic kernels ⋮ Fractional derivatives and the fundamental theorem of fractional calculus ⋮ Erdélyi-Kober fractional integrals and Radon transforms for mutually orthogonal affine planes ⋮ Index transforms with Weber-type kernels ⋮ The convolution for zero-order Mehler–Fock transform and pseudo-differential operator ⋮ A class of index transforms generated by the Mellin and Laplace operators ⋮ On a class of noncompact weakly singular Volterra integral equations: theory and application to fractional differential equations with variable coefficient ⋮ On a progress in the Kontorovich–Lebedev transform theory and related integral operators ⋮ On the Kontorovich-Lebedev transformation ⋮ Fourier–Jacobi harmonic analysis and some problems of approximation of functions on the half-axis in L₂ metric: Jackson's type direct theorems ⋮ On the orthogonality and convolution orthogonality via the Kontorovich-Lebedev transform ⋮ A convolution family in the Dimovski sense for the composed Erdélyi-Kober fractional integrals ⋮ On the half-Hartley transform, its iteration and compositions with Fourier transforms ⋮ An identity involving integration with respect to variable order of fractional derivative ⋮ Spectral Collocation Method for a Class of Integro-Differential Equations with Erdelyi-Kober Fractional Operator ⋮ Index transforms with the squares of Kelvin functions ⋮ Operational calculus for Caputo fractional calculus with respect to functions and the associated fractional differential equations ⋮ Lebedev type index transforms with the squares of the associated {L}egendre functions ⋮ Operational Calculus for Bessel’s Fractional Equation ⋮ On the WatsonL₂-theory for index transforms I ⋮ On perturbed fractional differential inclusions with nonlocal multi-point Erdélyi-Kober fractional integral boundary conditions ⋮ The Fourier-Stieltjes transform of Minkowskis \(?(x)\) function and an affirmative answer to Salem's problem ⋮ A class of integral equations and index transformations related to the modified and incomplete Bessel functions ⋮ On the least values of \(L_{p}\)-norms for the Kontorovich--Lebedev transform and its convolution ⋮ Asymptotic expansion of a Bessel function integral using hypergeometric functions ⋮ The solvability and explicit solutions of two integral equations via generalized convolutions ⋮ On the WatsonL₂-theory for index transforms II ⋮ Equivalence of K-functionals and modulus of smoothness constructed by generalized Jacobi transform ⋮ A unified construction of product formulas and convolutions for Sturm-Liouville operators ⋮ Fractional Klein-Gordon equations and related stochastic processes ⋮ Pathway fractional integral operator associated with 3m-parametric Mittag-Leffler functions ⋮ Discrete index Whittaker transforms ⋮ Operational calculus for the general fractional derivative and its applications ⋮ Operational calculus for the Riemann-Liouville fractional derivative with respect to a function and its applications ⋮ Some composition formulae for the M-S-M fractional integral operator with the multi-index Mittag-Leffler functions ⋮ Fourier–Jacobi harmonic analysis and some problems of approximation of functions on the half-axis in L₂ metric: Nikol'skii–Besov type function spaces ⋮ On an extension of the Mikusiński type operational calculus for the Caputo fractional derivative ⋮ Orthogonal polynomials with the Prudnikov-type weights ⋮ On the stabilization of the inversion of some Kontorovich-Lebedev like integral transforms ⋮ Index transforms with the product of the associated Legendre functions ⋮ Regularity of the solution to Riesz-type fractional differential equation ⋮ Composition method for constructing convolutions for integral transforms ⋮ Zero-order Mehler-Fock transform and Sobolev-type space ⋮ Subordination principles for the multi-dimensional space-time-fractional diffusion-wave equation ⋮ The convolution product is for exponential kernels transforms. Composition is suggested for other transforms ⋮ On the Laguerre fractional integro-differentiation ⋮ Lebedev–Skalskaya transforms on certain function spaces and associated pseudo-differential operators ⋮ The probabilistic point of view on the generalized fractional partial differential equations ⋮ Properties of index transforms in modeling of nanostructures and plasmonic systems ⋮ Use of fractional calculus to evaluate some improper integrals of special functions ⋮ Lévy processes with respect to the Whittaker convolution ⋮ The Kontorovich-Lebedev Transform as a Map betweend-Orthogonal Polynomials ⋮ Localization operators associated with the Kontorovich-Lebedev wavelet transform ⋮ Discrete orthogonal polynomials associated with Macdonald functions ⋮ On the generalized Lebedev index transform ⋮ From the hyper-Bessel operators of Dimovski to the generalized fractional calculus ⋮ A family of hyper-Bessel functions and convergent series in them ⋮ The Mellin integral transform in fractional calculus ⋮ Science metrics on fractional calculus development since 1966 ⋮ A Class of Index Transforms with General Kernels ⋮ A general class of integral transforms and an expression for their convolution formulas ⋮ Integrability of the Fourier–Jacobi transform of functions satisfying Lipschitz and Dini–Lipschitz-type estimates ⋮ Existence and uniqueness results for generalized Caputo iterative fractional boundary value problems

This page was built for publication: