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DEGENERATE DISTRIBUTED CONTROL SYSTEMS WITH FRACTIONAL TIME DERIVATIVE [PDF]

Ural Mathematical Journal, 2016
The existence of a unique strong solution for the Cauchy problem to semilinear nondegenerate fractional differential equation and for the generalized Showalter–Sidorov problem to semilinear fractional differential equation with degenerate operator at the
Marina V. Plekhanova
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Vibration Systems with Fractional-Order and Distributed-Order Derivatives Characterizing Viscoinertia [PDF]

Fractal and Fractional, 2021
We considered forced harmonic vibration systems with the Liouville–Weyl fractional derivative where the order is between 1 and 2 and with a distributed-order derivative where the Liouville–Weyl fractional derivatives are integrated on the interval [1, 2]
Jun-Sheng Duan, Di-Chen Hu
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Time fractional Saint Venant equations reveal the physical basis of hydrograph retardation through model comparison and field data [PDF]

Scientific Reports
River hydrodynamics are influenced by numerous factors that traditional models often fail to fully capture. Simulating complex hydrographs can benefit from parsimonious upscaling models, such as fractional derivative equations, that reduce the need to ...
Hui Wei, Song Wei, Qi Wang, HongGuang Sun, Jonathan Frame, Yong Zhang   +5 more
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Generalized boundary value problem for a linear ordinary differential equation with a discretely distributed fractional differentiation operator [PDF]

Қарағанды университетінің хабаршысы. Математика сериясы, 2022
This paper formulates and solves a generalized boundary value problem for a linear ordinary differential equation with a discretely distributed fractional differentiation operator.
L.Kh. Gadzova
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On the Solvability of Equations with a Distributed Fractional Derivative Given by the Stieltjes Integral

Mathematics, 2022
Linear equations in Banach spaces with a distributed fractional derivative given by the Stieltjes integral and with a closed operator A in the right-hand side are considered. Unlike the previously studied classes of equations with distributed derivatives,
Sergey M. Sitnik, Vladimir E. Fedorov, Nikolay V. Filin, Viktor A. Polunin   +3 more
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A computational approach based on the fractional Euler functions and Chebyshev cardinal functions for distributed-order time fractional 2D diffusion equation

Alexandria Engineering Journal, 2023
In this paper, the distributed-order time fractional diffusion equation is introduced and studied. The Caputo fractional derivative is utilized to define this distributed-order fractional derivative.
M.H. Heydari, M. Hosseininia, D. Baleanu
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Chelyshkov polynomials method for distributed-order time fractional nonlinear diffusion-wave equations

Results in Physics, 2023
This work deals with the distributed-order time fractional nonlinear diffusion-wave equations. These equations are generated by replacing the first- and second-order time derivative terms with the distributed-order fractional derivative terms.
M.H. Heydari, S. Rashid, Yu-Ming Chu
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Fractional diffusion: recovering the distributed fractional derivative from overposed data [PDF]

Inverse Problems, 2017
There has been considerable recent study in "sub-diffusion" models that replace the standard parabolic equation model by a one with a fractional derivative in the time variable. There are many ways to look at this newer approach and one such is to realize that the order of the fractional derivative is related to the time scales of the underlying ...
Rundell, W., Zhang, Z.
openaire   +2 more sources

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
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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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