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Fractional Calculus - Theory and Applications

, 2022
In recent years, fractional calculus has led to tremendous progress in various areas of science and mathematics. New definitions of fractional derivatives and integrals have been uncovered, extending their classical definitions in various ways. Moreover,

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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
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Research on Rock Creep Characteristics Based on the Fractional Calculus Meshless Method

Advances in Civil Engineering, 2018
The application of fractional calculus in the rheological problems has been widely accepted. In this study, the constitutive relationship of the generalized Kelvin model based on fractional calculus was studied, and the meshless method was introduced so ...
Gang Peng, Zhanqing Chen, Jiarui Chen
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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
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N-FRACTIONAL CALCULUS OPERATOR METHOD TO THE EULER EQUATION

Проблемы анализа, 2018
We can obtain the explicit solutions of the Euler equation by using the fractional calculus methods. So, we apply the N operator method in the fractional calculus to solve this equation in this paper.
R. Yilmazer, O. Ozturk
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Fractional Order Sequential Minimal Optimization Classification Method

Fractal and Fractional, 2023
Sequential minimal optimization (SMO) method is an algorithm for solving optimization problems arising from the training process of support vector machines (SVM).
Chunna Zhao, Licai Dai, Yaqun Huang
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Fractional variational problems depending on indefinite integrals [PDF]

, 2012
We obtain necessary optimality conditions for variational problems with a Lagrangian depending on a Caputo fractional derivative, a fractional and an indefinite integral.
Pooseh, Shakoor, Pooseh, S., Almeida, R., Almeida, Ricardo, Delfim F.M. Torres, Shakoor Pooseh, Torres, D.F.M., Ricardo Almeida, Torres, Delfim F. M.   +8 more
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An approximate analytical solution of the time-fractional Navier–Stokes equations by the generalized Laplace residual power series method

Partial Differential Equations in Applied Mathematics
The dynamics of viscous fluids may be elucidated via the Navier–Stokes equations, which create a fundamental relationship between the exertion of external forces upon fluid motion and the resultant fluid pressure.
P. Dunnimit, W. Sawangtong, P. Sawangtong   +2 more
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An analytical solution to the time fractional Navier–Stokes equation based on the Katugampola derivative in Caputo sense by the generalized Shehu residual power series approach

Partial Differential Equations in Applied Mathematics
The Navier–Stokes equations describe the behavior of viscous fluids and establish a fundamental connection between the application of external forces on fluid motion and the resulting pressure within the fluid. The objective of this study is to solve the
W. Sawangtong, P. Dunnimit, B. Wiwatanapataphee, P. Sawangtong   +3 more
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Implementation of fractional order integrator/differentiator on field programmable gate array

Alexandria Engineering Journal, 2016
Concept of fractional order calculus is as old as the regular calculus. With the advent of high speed and cost effective computing power, now it is possible to model the real world control and signal processing problems using fractional order calculus ...
K.P.S. Rana, V. Kumar, N. Mittra, N. Pramanik   +3 more
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