Results 11 to 20 of about 12,358 (240)

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   +2 more sources

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   +2 more sources

Fractional Vector Calculus and Fractional Maxwell's Equations [PDF]

, 2008
The theory of derivatives and integrals of non-integer order goes back to Leibniz, Liouville, Grunwald, Letnikov and Riemann. The history of fractional vector calculus (FVC) has only 10 years. The main approaches to formulate a FVC, which are used in the
V. E. Tarasov
semanticscholar   +3 more sources

Non-Additivity and Additivity in General Fractional Calculus and Its Physical Interpretations

Fractal and Fractional
In this work, some properties of the general convolutional operators of general fractional calculus (GFC), which satisfy analogues of the fundamental theorems of calculus, are described. Two types of general fractional (GF) operators on a finite interval
Vasily E. Tarasov
doaj   +2 more sources

A New Generalized Definition of Fractal–Fractional Derivative with Some Applications

Mathematical and Computational Applications
In this study, a new generalized fractal–fractional (FF) derivative is proposed. By applying this definition to some elementary functions, we show its compatibility with the results of the FF derivative in the Caputo sense with the power law.
Francisco Martínez, Mohammed K. A. Kaabar   +1 more
doaj   +2 more sources

General Fractional Economic Dynamics with Memory

Mathematics
For the first time, a self-consistent mathematical approach to describe economic processes with a general form of a memory function is proposed. In this approach, power-type memory is a special case of such general memory.
Vasily E. Tarasov
doaj   +2 more sources

APPLICATIONS OF TWO IMPORTANT THEOREMS OF FRACTIONAL CALCULUS

2021 INTERNATIONAL CONFERENCE ON ADVANCED EDUCATION AND INFORMATION MANAGEMENT (AEIM 2021), 2021
. In this article, we study the fundamental theorem of fractional calculus and integration by parts for fractional calculus, regarding the Jumarie type of modified Riemann-Liouville fractional derivatives. On the other hand, some examples are proposed to
Chii-Huei Yu
semanticscholar   +1 more source

Fractional Derivatives and the Fundamental Theorem of Fractional Calculus [PDF]

Fractional Calculus and Applied Analysis, 2020
In this paper, we address the one-parameter families of the fractional integrals and derivatives defined on a finite interval. First we remind the reader of the known fact that under some reasonable conditions, there exists precisely one unique family of the fractional integrals, namely, the well-known Riemann-Liouville fractional integrals.
openaire   +3 more sources

Study of Fractional Analytic Functions and Local Fractional Calculus

International Journal of Scientific Research in Science Engineering and Technology, 2021
In this present paper, the role of fractional analytic function in local fractional calculus is studied. Some important properties and theorems in local fractional calculus are discussed, such as product rule, quotient rule, chain rule, fundamental ...
Chii-Huei Yu
semanticscholar   +1 more source

General Fractional Integrals and Derivatives of Arbitrary Order [PDF]

Symmetry, 2021
In this paper, we introduce the general fractional integrals and derivatives of arbitrary order and study some of their basic properties and particular cases.
Yuri Luchko
semanticscholar   +1 more source