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Generalising the fractional calculus with Sonine kernels via conjugations

Journal of Computational and Applied Mathematics, 2023
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Mohammed Al-Refai, Arran Fernández
exaly   +3 more sources

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Fractional differential equations with continuous variable coefficients and Sonine kernels

Communications in Nonlinear Science and Numerical Simulation
We study linear fractional ODEs with continuous variable coefficients and general fractional derivative (GFD) operators of Riemann-Liouville and Caputo types defined using Sonine kernels. Using the Banach fixed point theorem, we prove existence and uniqueness of solution functions in suitable function spaces, and we construct these solutions explicitly
Arran Fernández, Nazim Mahmudov
exaly   +2 more sources

An equivalent formulation of Sonine condition [PDF]

Applied Mathematics Letters
Sonine kernel is characterized by the Sonine condition (denoted by SC) and is an important class of kernels in nonlocal differential equations and integral equations.
Xiangcheng Zheng
exaly   +2 more sources

Multi-dimensional Operators with Sonine Kernels

Trends in Mathematics
Arran Fernández
exaly   +2 more sources

Sonine—Gegenbauer-type integrals [PDF]

Journal of Computational and Applied Mathematics, 1994
Representations for complete and incomplete Sonine—Gegenbauer-type integrals are given in terms of generalized hypergeometric functions in two and three variables and in terms of Neumann-type series.
Allen R Miller
exaly   +2 more sources

Breakdown of the Sonine expansion for the velocity distribution of granular gases

Europhysics Letters, 2006
The velocity distribution of a granular gas is analyzed in terms of the Sonine polynomials expansion. We derive an analytical expression for the third Sonine coefficient a3.
Thorsten Pöschel, Nikolay Brilliantov
exaly   +2 more sources

Weighted 1st-level fractional derivatives with Sonine Kernels with respect to functions

Computational and Applied Mathematics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mahendrakumar N. Dabhi, Krunal B. Kachhia   +1 more
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Fuzzy general fractional operators with Sonine kernels under gH-differentiability

Computational and Applied Mathematics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xuelong Liu, Guoju Ye, Wei Liu 0088
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On the fractional-in-time Keller-Segel model via Sonine kernels

Topological Methods in Nonlinear Analysis
In this paper, we study the existence and asymptotic behavior to a diffusion system which is non-local in time. As consequence of our theorems we deduce new results for the fractional-in-time Keller-Segel model. Our approach is intimately related with the Sonine kernels.
Masterson Costa, Claudio Cuevas, Clessius Silva, Herme Soto   +3 more
openaire   +1 more source