Results 1 to 10 of about 43 (38)

Stability of Delay Hopfield Neural Networks with Generalized Riemann–Liouville Type Fractional Derivative [PDF]

Entropy, 2023
The general delay Hopfield neural network is studied. We consider the case of time-varying delay, continuously distributed delays, time-varying coefficients, and a special type of a Riemann–Liouville fractional derivative (GRLFD) with an exponential ...
Ravi P. Agarwal, Snezhana Hristova
doaj   +2 more sources

General Fractional Integrals and Derivatives with the Sonine Kernels

Mathematics, 2021
In this paper, we address the general fractional integrals and derivatives with the Sonine kernels on the spaces of functions with an integrable singularity at the point zero.
Yuri Luchko
doaj   +3 more sources

Sonine Transform Associated to the Dunkl Kernel on the Real Line [PDF]

Symmetry, Integrability and Geometry: Methods and Applications, 2008
We consider the Dunkl intertwining operator V_α and its dual ^tV_α, we define and study the Dunkl Sonine operator and its dual on R. Next, we introduce complex powers of the Dunkl Laplacian Δ_α and establish inversion formulas for the Dunkl Sonine ...
Fethi Soltani
doaj   +5 more sources

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   +2 more sources

On the Rigorous Correspondence Between Operator Fractional Powers and Fractional Derivatives via the Sonine Kernel

Fractal and Fractional
Traditional operational calculus, while intuitive and effective in addressing problems in physical fractal spaces, often lacks the rigorous mathematical foundation needed for fractional operations, sometimes resulting in inconsistent outcomes. To address
Zelin Liu, Xiaobin Yu, Yajun Yin
doaj   +2 more sources

Nonexistence of Finite-Time Stable Equilibria in a Class of Nonlinear Integral Equations

Fractal and Fractional, 2023
This brief report studies conditions to ensure the nonexistence of finite-time stable equilibria in a class of systems that are described by means of nonlinear integral equations, whose kernels are part of some Sonine kernel pairs.
Aldo Jonathan Muñoz-Vázquez, Oscar Martinez-Fuentes, Guillermo Fernández-Anaya   +2 more
doaj   +1 more source

Special Functions of Fractional Calculus in the Form of Convolution Series and Their Applications

Mathematics, 2021
In this paper, we first discuss the convolution series that are generated by Sonine kernels from a class of functions continuous on a real positive semi-axis that have an integrable singularity of power function type at point zero.
Yuri Luchko
doaj   +1 more source

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

Fractional Calculus in Russia at the End of XIX Century

Mathematics, 2021
In this survey paper, we analyze the development of Fractional Calculus in Russia at the end of the XIX century, in particular, the results by A. V. Letnikov, N. Ya. Sonine, and P. A. Nekrasov.
Sergei Rogosin, Maryna Dubatovskaya
doaj   +1 more source

Operational Calculus for the General Fractional Derivatives of Arbitrary Order

Mathematics, 2022
In this paper, we deal with the general fractional integrals and the general fractional derivatives of arbitrary order with the kernels from a class of functions that have an integrable singularity of power function type at the origin.
Maryam Al-Kandari, Latif A-M. Hanna, Yuri Luchko   +2 more
doaj   +1 more source