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General Fractional Calculus Operators with the Sonin kernels and Some of Their Applications

IFAC-PapersOnLine
openaire   +1 more source

General fractional q-integrals and q-derivatives: a Sonin–Luchko q-kernel approach

Arabian Journal of Mathematics
openaire   +1 more source

Generalising the Fractional Calculus With Sonine Kernels via Conjugations

Journal of Computational and Applied Mathematics, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mohammed Al-Refai, Arran Fernandez
exaly   +3 more sources

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.
Clessius Silva, Claudio Cuevas, Herme Soto   +2 more
exaly   +3 more sources

Extending Sonine Kernels to Arbitrary Dimensions

Banach Journal of Mathematical Analysis
Abstract The theory of general fractional calculus with Sonine kernels has been well developed by Luchko in the one-dimensional case. Inspired by recent work on Mikusiński’s operational calculus for fractional partial differential operators, we construct a multi-dimensional version of the theory of Sonine kernels, solving a recognised open ...
Arran Fernandez
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

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Multi-Dimensional Operators With Sonine Kernels

Trends in Mathematics
Arran Fernandez
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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 Fernandez, Nazim Mahmudov
exaly   +2 more sources

Fuzzy General Fractional Operators With Sonine Kernels Under gH-Differentiability

Computational and Applied Mathematics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guoju Ye
exaly   +3 more sources