Results 21 to 30 of about 2,430,235 (99)

Fractional Differential Equations with the General Fractional Derivatives of Arbitrary Order in the Riemann–Liouville Sense

Mathematics, 2022
In this paper, we first consider the general fractional derivatives of arbitrary order defined in the Riemann–Liouville sense. In particular, we deduce an explicit form of their null space and prove the second fundamental theorem of fractional calculus ...
Yuri Luchko
doaj   +1 more source

Generalising the fractional calculus with Sonine kernels via conjugations

, 2023
Many different types of fractional calculus are defined by various kernel functions within the general class of Sonine-type kernels, while many others are given by conjugating the usual fractional calculus with invertible linear operators, such as ...
Arran Fernandez, Fernandez, Arran, Al-Refai, Mohammed, Mohammed Al-Refai   +3 more
core   +1 more source

On generalized fractional differential equation with Sonine kernel on a function space

Partial Differential Equations in Applied Mathematics
Sonine kernel is a special type of the general kernels, satisfying some integrability and monotonicity conditions and properties. Sonine kernels generate some convolution polynomials (power functions) used in the construction of the general fractional ...
McSylvester Ejighikeme Omaba
doaj   +1 more source

Sonine integral equations [PDF]

, 2006
As equações integrais de Sonine são equações de primeira espécie, de Volterra, Kfp =f , com núcleo às diferenças, tais que existe um núcleo associado ao núcleo original de modo que sejam ambos divisores da unidade para a convolução.
Cardoso, Rogério Pereira
core   +1 more source

Beta distributions and Sonine integrals for Bessel functions on symmetric cones [PDF]

, 2018
There exist several multivariate extensions of the classical Sonine integral representation for Bessel functions of some index μ + v with respect to such functions of lower index μ.
Voit, Michael, Rösler, Margit
core   +1 more source

Summing Sneddon–Bessel series explicitly

Mathematical Methods in the Applied Sciences, Volume 47, Issue 7, Page 6590-6606, 15 May 2024.
We sum in a closed form the Sneddon–Bessel series ∑m=1∞Jα(xjm,ν)Jβ(yjm,ν)jm,ν2n+α+β−2ν+2Jν+1(jm,ν)2,$$ \sum \limits_{m=1}^{\infty}\frac{J_{\alpha}\left(x{j}_{m,\nu}\right){J}_{\beta}\left(y{j}_{m,\nu}\right)}{j_{m,\nu}^{2n+\alpha +\beta -2\nu +2}{J}_{\nu +1}{\left({j}_ ...
Antonio J. Durán, Mario Pérez, Juan Luis Varona   +2 more
wiley   +1 more source

Inversion of the Dual Dunkl-Sonine Transform on R Using Dunkl Wavelets [PDF]

, 2009
We prove a Calderón reproducing formula for the Dunkl continuous wavelet transform on R.
Mohamed Ali Mourou
core   +2 more sources

Prolate spheroidal wave functions, Sonine spaces, and the Riemann zeta function [PDF]

, 2012
In this paper we study underlying spaces associated with A. Connesʼ trace formula (see Connes (1999) [3], Li (2010) [14]). In particular the explicit formula in the theory of prime numbers is expressed as the trace of an operator acting on a Hilbert ...
Li, Xian-Jin, Xian-Jin Li
core   +1 more source

S. N. Bose (1894‐1974) and the Bose quantum statistics a centennial tribute

, 1993
International Journal of Mathematics and Mathematical Sciences, Volume 16, Issue 4, Page 625-644, 1993.
Lokenath Debnath
wiley   +1 more source

On a q-Dunkl sonine transform [PDF]

, 2013
In this paper, we introduce and study the q-Dunkl Sonine transform and we establish a Plancherel formula for its dual.
Bettaieb, Rym Hasna, Bennasr, Lassad, Nouri, Ferjani   +2 more
core   +1 more source