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
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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
Optimization with Respect to Order in a Fractional Diffusion Model: Analysis, Approximation and Algorithmic Aspects
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DOI: 10.1007/s10915-018-0703-0
Abstract: We consider an identification (inverse) problem, where the state $${\mathsf {u}}$$u is governed by a fractional elliptic equation and the unknown variable corresponds to the order $$s \in (0,1)$$s∈(0,1) of the underlying operator. We study… read more here.
Keywords: fractional diffusion; optimization respect; respect order; order ... See more keywords
Non-linear System of Multi-order Fractional Differential Equations: Theoretical Analysis and a Robust Fractional Galerkin Implementation
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DOI: 10.1007/s10915-022-01814-x
Abstract: This paper presents a comprehensive study of non-linear systems of multi-order fractional differential equations from aspects of theory and numerical approximation. In this regard, we first establish the well-posedness of the underlying problem by investigations… read more here.
Keywords: order fractional; order; non linear; multi order ... See more keywords
A triaxial creep model for salt rocks based on variable-order fractional derivative
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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
A Legendre collocation method for distributed-order fractional optimal control problems
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DOI: 10.1007/s11071-017-4038-4
Abstract: In many dynamic processes, the fractional differential operators not only appear as discrete fractional, but they also possess a continuous nature in a sense that their order is distributed over a given range. This paper… read more here.
Keywords: distributed order; order; method; order fractional ... See more keywords
Application of variable- and distributed-order fractional operators to the dynamic analysis of nonlinear oscillators
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DOI: 10.1007/s11071-020-05488-8
Abstract: Many physical processes in nature exhibit complex dynamics that result from a combination of multiscale, nonlinear, non-local, and memory effects. Recent experimental measurements conducted in a variety of physical domains have shown that, at the… read more here.
Keywords: distributed order; order; fractional operators; application variable ... 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
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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
A Caputo variable-order fractional damage creep model for sandstone considering effect of relaxation time
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DOI: 10.1007/s11440-021-01230-9
Abstract: Establishing a fractional creep model with few parameters and explicit physical interpretation is of significant meaning for predicting rheological deformation of rock. In this study, based on the Caputo variable-order fractional derivative, a Caputo variable-order… read more here.
Keywords: caputo variable; order; creep model; damage ... See more keywords
Variable order fractional integrals in variable generalized Hölder spaces of holomorphic functions
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DOI: 10.1007/s13324-021-00587-0
Abstract: We introduce and study the variable generalized Holder spaces of holomorphic functions over the unit disc in the complex plane. These spaces are defined either directly in terms of modulus of continuity or in terms… read more here.
Keywords: variable generalized; fractional integrals; holomorphic functions; spaces holomorphic ... See more keywords