Results 31 to 40 of about 1,386 (256)

Generalized Euler-Lagrange Equations for Fuzzy Fractional Variational Problems under gH-Atangana-Baleanu Differentiability

Journal of Function Spaces, 2018
We study in this paper the Atangana-Baleanu fractional derivative of fuzzy functions based on the generalized Hukuhara difference. Under the condition of gH-Atangana-Baleanu fractional differentiability, we prove the generalized necessary and sufficient ...
Jianke Zhang, Gaofeng Wang, Xiaobin Zhi, Chang Zhou   +3 more
doaj   +1 more source

Relationship Between the Nonlinear Oscillator and the Motor Cortex

IEEE Access, 2019
The investigations show that the fractional calculus could be employed for complex biological systems and capture intrinsic phenomena. At the same time, the research results also show that the neural network has the characteristics of fractional calculus
Qiang Lu
doaj   +1 more source

Weighted hypergeometric functions and fractional derivative

Advances in Difference Equations, 2017
We introduce some weighted hypergeometric functions and the suitable generalization of the Caputo fractional derivation. For these hypergeometric functions, some linear and bilinear relations are obtained by means of the mentioned derivation operator ...
JE Restrepo, A Kılıçman, P Agarwal, Omer Altun   +3 more
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An Expansion Formula with Higher-Order Derivatives for Fractional Operators of Variable Order

The Scientific World Journal, 2013
We obtain approximation formulas for fractional integrals and derivatives of Riemann-Liouville and Marchaud types with a variable fractional order. The approximations involve integer-order derivatives only. An estimation for the error is given.
Ricardo Almeida, Delfim F. M. Torres
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A Non-Integer High-Order Sliding Mode Control of Induction Motor with Machine Learning-Based Speed Observer

Machines, 2023
The induction motor (IM) drives are prone to various uncertainties, disturbances, and non-linear dynamics. A high-performance control system is essential in the outer loop to guarantee the accurate convergence of speed and torque to the required value ...
Irfan Sami, Shafaat Ullah, Shafqat Ullah, Syed Sabir Hussain Bukhari, Naseer Ahmed, Muhammad Salman, Jong-Suk Ro   +6 more
doaj   +1 more source

Fractional Calculus of Variations for Double Integrals

, 2011
We consider fractional isoperimetric problems of calculus of variations with double integrals via the recent modified Riemann-Liouville approach. A necessary optimality condition of Euler-Lagrange type, in the form of a multitime fractional PDE, is proved, as well as a sufficient condition and fractional natural boundary conditions.
Odzijewicz, T., Torres, D.F.M.
openaire   +3 more sources

Variational Problems with Time Delay and Higher-Order Distributed-Order Fractional Derivatives with Arbitrary Kernels

Mathematics, 2021
In this work, we study variational problems with time delay and higher-order distributed-order fractional derivatives dealing with a new fractional operator.
Fátima Cruz, Ricardo Almeida, Natália Martins   +2 more
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Quantum Mechanics and Control Using Fractional Calculus: A Study of the Shutter Problem for Fractional Quantum Fields

Applied Mechanics, 2022
The ‘diffraction in space’ and the ‘diffraction in time’ phenomena are considered in regard to a continuously open, and a closed shutter that is opened at an instant in time, respectively.
Jonathan Blackledge
doaj   +1 more source

Optimizing Variational Problems through Weighted Fractional Derivatives

Fractal and Fractional
In this article, we explore a variety of problems within the domain of calculus of variations, specifically in the context of fractional calculus. The fractional derivative we consider incorporates the notion of weighted fractional derivatives along with
Ricardo Almeida
doaj   +1 more source

Optimal charging of fractional-order circuits with Cuckoo search

Journal of Advanced Research, 2021
Introduction: Optimal charging of RC circuits is a well-studied problem in the integer-order domain due to its importance from economic and system temperature hazards perspectives.
A.M. AbdelAty, Mohammed E. Fouda, Menna T.M.M. Elbarawy, A.G. Radwan   +3 more
doaj   +1 more source