Results 11 to 20 of about 283 (92)

General Fractional Calculus: Multi-Kernel Approach

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   +1 more source

On the Existence and Stability of a Neutral Stochastic Fractional Differential System

Fractal and Fractional, 2022
The main purpose of this paper is to investigate the existence and Ulam-Hyers stability (U-Hs) of solutions of a nonlinear neutral stochastic fractional differential system.
Manzoor Ahmad, Akbar Zada, Mehran Ghaderi, Reny George, Shahram Rezapour   +4 more
doaj   +1 more source

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
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Pathological study on uncertain numbers and proposed solutions for discrete fuzzy fractional order calculus

Open Physics, 2023
A pathological study in the definition of uncertain numbers is carried out, and some solutions are proposed. Fundamental theorems for uncertain discrete fractional and integer order calculus are established.
Shiri Babak, Baleanu Dumitru, Ma Chang-You   +2 more
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On the 1st-Level General Fractional Derivatives of Arbitrary Order

Fractal and Fractional, 2023
In this paper, the 1st-level general fractional derivatives of arbitrary order are defined and investigated for the first time. We start with a generalization of the Sonin condition for the kernels of the general fractional integrals and derivatives and ...
Yuri Luchko
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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
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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
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Stability of Delay Hopfield Neural Networks with Generalized Riemann–Liouville Type Fractional Derivative

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   +1 more source

FRACTAL RADIOPHYSICS. Part 3. FRACTIONAL CALCULUS IN ELECTRODYNAMICS [PDF]

Radio Physics and Radio Astronomy
Subject and Purpose. At the beginning of the 21st century, a fundamentally new scientific direction was formed, currently known as fractal radiophysics.
O. V. Lazorenko, L. F. Chernogor
doaj   +1 more source

Fractional Dynamics and Fixed Point Theorems in Neutrosophic MR-Metric Spaces with Applications to Network Systems [PDF]

Neutrosophic Sets and Systems
This paper introduces and analyzes the structure of Neutrosophic MR Metric Spaces (NMR-MS) and their graph-based variants, termed Neutrosophic Graph MR-Metric Spaces (NGMR-MS).
Abed Al-Rahman M. Malkawi, Ayat M. Rabaiah   +1 more
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