Results 21 to 30 of about 166,384,605 (228)

Fractional calculus of periodic distributions [PDF]

, 2011
Two approaches for defining fractional derivatives of periodic distributions are presented. The first is a distributional version of the Weyl fractional derivative in which a derivative of arbitrary order of a periodic distribution is defined via Fourier
Lamb, Wilson, Khan, Khaula Naeem, Mcbride, Adam   +2 more
core   +4 more sources

General Non-Local Continuum Mechanics: Derivation of Balance Equations

Mathematics, 2022
In this paper, mechanics of continuum with general form of nonlocality in space and time is considered. Some basic concepts of nonlocal continuum mechanics are discussed. General fractional calculus (GFC) and general fractional vector calculus (GFVC) are
Vasily E. Tarasov
doaj   +1 more source

CONSTRUCTION OF FUNDAMENTAL THEOREMS OF FRACTIONAL CALCULUS [PDF]

Journal of Fundamental Mathematics and Applications (JFMA)
This paper discusses the theory of derivatives and integrals in the form of fractions with a particular order initiated by Lioville. Specifically, regarding the correlation between fractional derivatives and integrals, by examining definitions ...
Khairunnisa Fadhilla Ramdhania, Rafika Sari, Rakhmi Khalida, Aldira Ryan Pratama, Nur’aini Puji Lestari   +4 more
openaire   +2 more sources

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

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
doaj   +1 more source

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
doaj   +1 more source

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

Fractional Versions of the Fundamental Theorem of Calculus

Applied Mathematics, 2013
The concept of fractional integral in the Riemann-Liouville, Liouville, Weyl and Riesz sense is presented. Some properties involving the particular Riemann-Liouville integral are mentioned. By means of this concept we present the fractional derivatives, specifically, the Riemann-Liouville, Liouville, Caputo, Weyl and Riesz versions are discussed.
Eliana Contharteze Grigoletto, Edmundo Capelas de Oliveira   +1 more
openaire   +2 more sources

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