Results 1 to 10 of about 487,487 (101)

On Symmetrical Sonin Kernels in Terms of Hypergeometric-Type Functions

Mathematics
In this paper, a new class of kernels of integral transforms of the Laplace convolution type that we named symmetrical Sonin kernels is introduced and investigated.
Yuri Luchko
doaj   +6 more sources

Anomalous Diffusion Models Involving Regularized General Fractional Derivatives with Sonin Kernels

Fractal and Fractional
In this paper, we introduce a general fractional master equation involving regularized general fractional derivatives with Sonin kernels, and we discuss its physical characteristics and mathematical properties.
Maryam Alkandari, Dimitri Loutchko, Yuri Luchko   +2 more
doaj   +6 more sources

On Solvability of the Sonin–Abel Equation in the Weighted Lebesgue Space

Fractal and Fractional, 2021
In this paper we present a method of studying a convolution operator under the Sonin conditions imposed on the kernel. The particular case of the Sonin kernel is a kernel of the fractional integral Riemman–Liouville operator, other various types of the ...
Maksim V. Kukushkin
doaj   +5 more sources

General Fractional Calculus Operators of Distributed Order

Axioms, 2023
In this paper, two types of general fractional derivatives of distributed order and a corresponding fractional integral of distributed type are defined, and their basic properties are investigated.
Mohammed Al-Refai, Yuri Luchko
doaj   +5 more sources

General Non-Markovian Quantum Dynamics [PDF]

Entropy, 2021
A general approach to the construction of non-Markovian quantum theory is proposed. Non-Markovian equations for quantum observables and states are suggested by using general fractional calculus.
Vasily E. Tarasov
doaj   +3 more sources

General Fractional Calculus: Multi-Kernel Approach [PDF]

Mathematics, 2021
For the first time, a general fractional calculus of arbitrary order was proposed by Yuri Luchko in 2021. In Luchko works, the proposed approaches to formulate this calculus are based either on the power of one Sonin kernel or the convolution of one ...
Vasily E. Tarasov
doaj   +3 more sources

Searching for Sonin Kernels

Fractional Calculus and Applied Analysis
AbstractThe causal shift-invariant convolution is studied from the point of view of inversion. Abel’s algorithm, used in the tautochrone problem, is considered and Sonin’s existence condition is deduced. To generate pairs of functions verifying Sonin’s condition, the class of Mittag-Leffler type functions is used.
Gabriel Bengochea, Manuel D Ortigueira
exaly   +4 more sources

General Fractional Dynamics [PDF]

Mathematics, 2021
General fractional dynamics (GFDynamics) can be viewed as an interdisciplinary science, in which the nonlocal properties of linear and nonlinear dynamical systems are studied by using general fractional calculus, equations with general fractional ...
Vasily E. Tarasov
doaj   +2 more sources

On a Gronwall-Type Inequality for the General Fractional Integrals With the Sonin Kernels and Its Applications

Communications in Nonlinear Science and Numerical Simulation
Mohammed Al-Refai, Mohammadkheer Al-Jararha, Yuri Luchko   +2 more
exaly   +3 more sources

General Fractional Calculus Operators With the Sonin Kernels and Some of Their Applications

IFAC-PapersOnLine
Yuri Luchko
exaly   +3 more sources