Well‐posedness of degenerate differential equations with fractional derivative in vector‐valued functional spaces
Sign Up to like & getrecommendations! Published in 2017 at "Mathematische Nachrichten"
DOI: 10.1002/mana.201500481
Abstract: In this paper, we study the well-posedness of the degenerate differential equations with fractional derivative Dα(Mu)(t)=Au(t)+f(t),(0≤t≤2π) in Lebesgue–Bochner spaces Lp(T;X), periodic Besov spaces Bp,qs(T;X) and periodic Triebel–Lizorkin spaces Fp,qs(T;X), where A and M are closed… read more here.
Keywords: degenerate differential; well posedness; fractional derivative; posedness degenerate ... See more keywords
Regularity results for fractional diffusion equations involving fractional derivative with Mittag–Leffler kernel
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DOI: 10.1002/mma.6459
Abstract: This paper studies partial differential equation model with the new general fractional derivatives involving the kernels of the extended Mittag–Leffler type functions. An initial boundary value problem for the anomalous diffusion of fractional order is… read more here.
Keywords: fractional derivative; mittag leffler; derivative mittag; diffusion ... See more keywords
On solvability of differential equations with the Riesz fractional derivative
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DOI: 10.1002/mma.7773
Abstract: We consider the solvability of fractional differential equations involving the Riesz fractional derivative. Our approach basically relies on the reduction of the problem considered to the equivalent nonlinear mixed Volterra and Cauchy‐type singular integral equation… read more here.
Keywords: fractional derivative; solvability differential; riesz fractional; equations riesz ... See more keywords
Steady-state non-linear vibrations of plates using Zener material model with fractional derivative
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DOI: 10.1007/s00466-017-1408-1
Abstract: The paper is devoted to non-linear vibrations of plates, made of the Zener viscoelastic material modelled with the Caputo fractional derivative, and in particular to their response to harmonic excitation. The plate geometric non-linearity is… read more here.
Keywords: linear vibrations; non linear; fractional derivative; plate ... 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
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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
Fractional derivative in the elastic-viscoplastic stress-strain state model describing anisotropic creep of soft clays
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DOI: 10.1007/s11043-020-09480-y
Abstract: A fractional elastic-viscoplastic (F-EVP) creep model describing the anisotropy of soft soil is established. A nonlinear viscoplastic creep expression is obtained by a fractional derivative and the Laplace transformation, which is extended by the definition… read more here.
Keywords: model describing; elastic viscoplastic; fractional derivative; model ... See more keywords
An epidemiological MSEIR model described by the Caputo fractional derivative
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DOI: 10.1007/s40435-018-0492-1
Abstract: A fractional MSEIR model is presented, involving the Caputo fractional derivative. The equilibrium points and the basic reproduction number are computed. An analysis of the local asymptotic stability at the disease free equilibrium is given.… read more here.
Keywords: fractional derivative; mseir model; caputo fractional; epidemiological mseir ... See more keywords
On a $$\psi $$-Generalized Fractional Derivative Operator of Riemann–Liouville with Some Applications
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DOI: 10.1007/s40819-020-00892-5
Abstract: Various extended beta functions have been investigated by many researchers (Mubeen et al. in FJMS 102:1545–1557, 2017; Ozergin et al. in J Comput Appl Math 235:4601–4610, 2011; Parmar et al. in J Class Anal 11:91–106,… read more here.
Keywords: fractional derivative; riemann liouville; derivative operator; psi generalized ... See more keywords
New explicit formulas for the some special matrices with fractional derivatives: II
Sign Up to like & getrecommendations! Published in 2020 at "Ain Shams Engineering Journal"
DOI: 10.1016/j.asej.2020.08.023
Abstract: Abstract Matrices have important applications of statistical analysis, circuits, mechanics, optics, and quantum physics. In this article, matrix explicit formulas of the exponentials for computing exp(αA), where A is a special n × n matrix and α… read more here.
Keywords: new explicit; fractional derivative; matrices fractional; special matrices ... See more keywords
High-order central difference scheme for Caputo fractional derivative
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DOI: 10.1016/j.cma.2016.12.008
Abstract: Abstract In this paper we propose a class of central difference schemes for resolving the Caputo fractional derivative. The accuracy may reach any selected integer order. More precisely, the Caputo fractional derivative operator is decomposed… read more here.
Keywords: order; fractional derivative; scheme; central difference ... See more keywords