Results 1 to 10 of about 6,699,757 (251)

Local Fuzzy Fractional Partial Differential Equations in the Realm of Fractal Calculus with Local Fractional Derivatives

Fractal and Fractional, 2023
In this study, local fuzzy fractional partial differential equations (LFFPDEs) are considered using a hybrid local fuzzy fractional approach. Fractal model behavior can be represented using fuzzy partial differential equations (PDEs) with local ...
Mawia Osman, Muhammad Marwan, Syed Omar Shah, Lamia Loudahi, Mahvish Samar, Ebrima Bittaye, Altyeb Mohammed Mustafa   +6 more
doaj   +4 more sources

Processing the Controllability of Control Systems with Distinct Fractional Derivatives via Kalman Filter and Gramian Matrix

Fractal and Fractional
In this paper, we investigate the controllability conditions of linear control systems involving distinct local fractional derivatives. Sufficient conditions for controllability using Kalman rank conditions and the Gramian matrix are presented.
Muath Awadalla, Abir Chaouk, Maher Jneid, Kinda Abuasbeh, Jihan Alahmadi   +4 more
doaj   +3 more sources

Nonlinear Fractional Evolution Control Modeling via Power Non-Local Kernels: A Generalization of Caputo–Fabrizio, Atangana–Baleanu, and Hattaf Derivatives

Fractal and Fractional
This paper presents a novel framework for modeling nonlinear fractional evolution control systems. This framework utilizes a power non-local fractional derivative (PFD), which is a generalized fractional derivative that unifies several well-known ...
F. Gassem, Mohammed Almalahi, Osman Osman, Blgys Muflh, Khaled Aldwoah, Alwaleed Kamel, Nidal Eljaneid   +6 more
doaj   +3 more sources

On Λ-Fractional Analysis and Mechanics

Axioms, 2022
Λ-Fractional analysis was introduced to fill up the mathematical gap exhibited in fractional calculus, where the various fractional derivatives fail to fulfill the prerequisites demanded by differential topology.
Konstantinos A. Lazopoulos
doaj   +1 more source

Fractional vs. Ordinary Control Systems: What Does the Fractional Derivative Provide?

Mathematics, 2022
The concept of a fractional derivative is not at all intuitive, starting with not having a clear geometrical interpretation. Many different definitions have appeared, to the point that the need for order has arisen in the field.
J. Alberto Conejero, Jonathan Franceschi, Enric Picó-Marco   +2 more
doaj   +1 more source

Orthonormal piecewise Vieta-Lucas functions for the numerical solution of the one- and two-dimensional piecewise fractional Galilei invariant advection-diffusion equations

Journal of Advanced Research, 2023
Introduction: Recently, a new family of fractional derivatives called the piecewise fractional derivatives has been introduced, arguing that for some problems, each of the classical fractional derivatives may not be able to provide an accurate statement ...
Mohammad Hossein Heydari, Mohsen Razzaghi, Dumitru Baleanu   +2 more
doaj   +1 more source

Fractal Stochastic Processes on Thin Cantor-Like Sets

Mathematics, 2021
We review the basics of fractal calculus, define fractal Fourier transformation on thin Cantor-like sets and introduce fractal versions of Brownian motion and fractional Brownian motion. Fractional Brownian motion on thin Cantor-like sets is defined with
Alireza Khalili Golmankhaneh, Renat Timergalievich Sibatov   +1 more
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On the fractional deformation of a linearly elastic bar

Journal of the Mechanical Behavior of Materials, 2020
Fractional derivatives have non-local character, although they are not mathematical derivatives, according to differential topology. New fractional derivatives satisfying the requirements of differential topology are proposed, that have non-local ...
Lazopoulos Konstantinos A., Lazopoulos Anastasios K.   +1 more
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A Class of Quasilinear Equations with Riemann–Liouville Derivatives and Bounded Operators

Axioms, 2022
The existence and uniqueness of a local solution is proved for the incomplete Cauchy type problem to multi-term quasilinear fractional differential equations in Banach spaces with Riemann–Liouville derivatives and bounded operators at them.
Vladimir E. Fedorov, Mikhail M. Turov, Bui Trong Kien   +2 more
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Dynamics and simulations of discretized Caputo-conformable fractional-order Lotka–Volterra models

Nonlinear Engineering, 2022
In this article, a prey–predator system is considered in Caputo-conformable fractional-order derivatives. First, a discretization process, making use of the piecewise-constant approximation, is performed to secure discrete-time versions of the two ...
Yousef Feras, Semmar Billel, Al Nasr Kamal   +2 more
doaj   +1 more source