A direct computational method for nonlinear variable‐order fractional delay optimal control problems
Sign Up to like & getrecommendations! Published in 2020 at "Asian Journal of Control"
DOI: 10.1002/asjc.2408
Abstract: This paper introduces a highly accurate operational matrix technique based upon the Chebyshev cardinal functions (CCFs) for solving a new category of nonlinear delay optimal control problems (OCPs) involving variable‐order (VO) fractional dynamical systems. The… read more here.
Keywords: delay; optimal control; delay optimal; variable order ... See more keywords
Numerical investigation of variable‐order fractional Benjamin–Bona–Mahony–Burgers equation using a pseudo‐spectral method
Sign Up to like & getrecommendations! Published in 2021 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.7297
Abstract: This article introduces a new local variable‐order (VO) fractional differentiation called the VO conformable fractional derivative. This derivative is employed to define the VO time fractional Benjamin–Bona–Mahony–Burgers (BBMB) equation. A pseudo‐spectral algorithm using the Chebyshev… read more here.
Keywords: order fractional; bona mahony; benjamin bona; method ... See more keywords
A modified variable‐order fractional SIR model to predict the spread of COVID‐19 in India
Sign Up to like & getrecommendations! Published in 2021 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.7655
Abstract: The first case of COVID-19 in India detected on January 30, 2020, after its emergence in Wuhan, China, in December 2019. The lockdown was imposed as anemergency measure by the Indian government to prevent the… read more here.
Keywords: sir model; fractional sir; sir; model ... See more keywords
An Adaptive Difference Method for Variable-Order Diffusion Equations
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DOI: 10.1007/s00009-024-02681-6
Abstract: An adaptive finite difference scheme for variable-order fractional-time subdiffusion equations in the Caputo form is studied. The fractional-time derivative is discretized by the L1 procedure but using nonhomogeneous timesteps. The size of these timesteps is… read more here.
Keywords: variable order; method; diffusion equations; difference ... See more keywords
On the variable-order fractional derivatives with respect to another function
Sign Up to like & getrecommendations! Published in 2024 at "Aequationes mathematicae"
DOI: 10.1007/s00010-024-01082-0
Abstract: In this paper, we present various concepts concerning generalized fractional calculus, wherein the fractional order of operators is not constant, and the integral kernel depends on a function. We observe that in the case of… read more here.
Keywords: variable order; order fractional; function; fractional derivatives ... See more keywords
Dynamic modeling of bone remodeling, osteolytic metastasis and PK/PD therapy: introducing variable order derivatives as a simplification technique.
Sign Up to like & getrecommendations! Published in 2021 at "Journal of mathematical biology"
DOI: 10.1007/s00285-021-01666-3
Abstract: Bone is constantly being renewed: in the adult skeleton, bone resorption and formation are in a tightly coupled balance, allowing for a constant bone density to be maintained. Yet this micro-environment provides the necessary conditions… read more here.
Keywords: bone; bone remodeling; therapy; variable order ... See more keywords
Approximation and application of the Riesz-Caputo fractional derivative of variable order with fixed memory
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DOI: 10.1007/s11012-021-01364-w
Abstract: In this paper, the Riesz-Caputo fractional derivative of variable order with fixed memory is considered. The studied non-integer differential operator is approximated by means of modified basic rules of numerical integration. The three proposed methods… read more here.
Keywords: derivative variable; riesz caputo; variable order; caputo fractional ... See more keywords
A triaxial creep model for salt rocks based on variable-order fractional derivative
Sign Up to like & getrecommendations! Published in 2020 at "Mechanics of Time-Dependent Materials"
DOI: 10.1007/s11043-020-09470-0
Abstract: This paper intend to describe the entire creep process of a salt rock under triaxial loading, especially the creep characteristics in the accelerated creep stage, by replacing the Newtonian dashpot in the Maxwell model with… read more here.
Keywords: variable order; salt rock; salt; model ... See more keywords
Enhanced FPGA realization of the fractional-order derivative and application to a variable-order chaotic system
Sign Up to like & getrecommendations! Published in 2020 at "Nonlinear Dynamics"
DOI: 10.1007/s11071-019-05449-w
Abstract: The efficiency of the hardware implementations of fractional-order systems heavily relies on the efficiency of realizing the fractional-order derivative operator. In this work, a generic hardware implementation of the fractional-order derivative based on the Grünwald–Letnikov’s… read more here.
Keywords: order; fractional order; application variable; order chaotic ... See more keywords
Adaptive control for discontinuous variable-order fractional systems with disturbances
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DOI: 10.1007/s11071-021-06199-4
Abstract: This paper deals with the global asymptotic stabilization and finite-time stabilization issues for variable-order fractional systems with partial a priori bounded disturbances by designing an appropriate adaptive controller. Via the inductive method and Arzela-Ascoli theorem,… read more here.
Keywords: fractional systems; adaptive control; order fractional; variable order ... See more keywords
Crank-Nicolson-weighted-shifted-Grünwald-difference schemes for space Riesz variable-order fractional diffusion equations
Sign Up to like & getrecommendations! Published in 2020 at "Numerical Algorithms"
DOI: 10.1007/s11075-020-00980-z
Abstract: In this paper, high-order finite difference methods are proposed to solve the initial-boundary value problem for space Riesz variable-order fractional diffusion equations. Based on weighted-shifted-Grünwald-difference (WSGD) operators proposed in Lin and Liu (J. Comput. Appl.… read more here.
Keywords: difference; order; space riesz; order fractional ... See more keywords