Results 11 to 20 of about 58,702 (266)

Advanced materials modelling via fractional calculus: challenges and perspectives. [PDF]

Philos Trans A Math Phys Eng Sci, 2020
Failla G, Zingales M.
europepmc   +2 more sources

Deformation of quantum mechanics in fractional-dimensional space [PDF]

, 2001
A new kind of deformed calculus (the D-deformed calculus) that takes place in fractional-dimensional spaces is presented. The D-deformed calculus is shown to be an appropriate tool for treating fractional-dimensional systems in a simple way and quite ...
A Matos-Abiague, Biedenharn L C, Chang Z, Chung K, Jarlskog C, Li Y, Macfarlane A J, Mandelbrot B B, Matos-Abiague A, Rosenblum M, Schäfer A, Stillinger F H, Sun C P, Torres J L   +13 more
core   +2 more sources

Some trapezoid and midpoint type inequalities via fractional ( p , q ) $(p,q)$ -calculus

Advances in Difference Equations, 2021
Fractional calculus is the field of mathematical analysis that investigates and applies integrals and derivatives of arbitrary order. Fractional q-calculus has been investigated and applied in a variety of research subjects including the fractional q ...
Pheak Neang, Kamsing Nonlaopon, Jessada Tariboon, Sotiris K. Ntouyas, Praveen Agarwal   +4 more
doaj   +1 more source

Foundations of generalized Prabhakar-Hilfer fractional calculus with applications

Cubo, 2021
Here we introduce the generalized Prabhakar fractional calculus and we also combine it with the generalized Hilfer calculus. We prove that the generalized left and right side Prabhakar fractional integrals preserve continuity and we find tight upper ...
George A. Anastassiou
doaj   +1 more source

Review of Some Promising Fractional Physical Models [PDF]

, 2015
Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law non-locality, power-law long-term memory or fractal properties by using integrations and ...
Tarasov, Vasily E.
core   +1 more source

Fractional Calculus [PDF]

, 2011
Fractional calculus: Models and numerical ...
BALEANU D, DIETHELM K, SCALAS, Enrico, TRUJILLO J. J.   +3 more
  +7 more sources

Motion Control of Autonomous Underwater Vehicle Based on Fractional Calculus Active Disturbance Rejection

Journal of Marine Science and Engineering, 2021
An active disturbance rejection control based on fractional calculus is proposed to improve the motion performance and robustness of autonomous underwater vehicle (AUV).
Junhe Wan, Hailin Liu, Jian Yuan, Yue Shen, Hao Zhang, Haoxiang Wang, Yi Zheng   +6 more
doaj   +1 more source

Maximum Principle for General Controlled Systems Driven by Fractional Brownian Motions [PDF]

, 2012
We obtain a maximum principle for stochastic control problem of general controlled stochastic differential systems driven by fractional Brownian motions (of Hurst parameter $H>1/2$). This maximum principle specifies a system of equations that the optimal
Han, Yuecai, Hu, Yaozhong, Song, Jian
core   +2 more sources

Weighted Fractional Calculus: A General Class of Operators

Fractal and Fractional, 2022
We conduct a formal study of a particular class of fractional operators, namely weighted fractional calculus, and its extension to the more general class known as weighted fractional calculus with respect to functions.
Arran Fernandez, Hafiz Muhammad Fahad
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