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Unexpected behavior of Caputo fractional derivative
(2017-09-01)
This paper discusses the modeling via mathematical methods based on fractional calculus, using Caputo fractional derivative. From the fractional models associated with harmonic oscillator, logistic equation and Malthusian ...
Linear differential equations of fractional order with recurrence relationship
(Natural Sciences Publishing, 2021-01)
This paper introduce the basic general theory for Linear Sequential Fractional Differential Equations which includes a recurrence relationship, involving the Riemann-Liouville fractional operator. The presented equation ...
Linear fractional differential equations and eigenfunctions of fractional differential operators
(2018-05-01)
Eigenfunctions associated with Riemann–Liouville and Caputo fractional differential operators are obtained by imposing a restriction on the fractional derivative parameter. Those eigenfunctions can be used to express the ...
Harvest Management Problem with a Fractional Logistic Equation
(Akadémiai Kiadó, 2021-10)
In this article, we study a fractional control problem that models the maximization of the profit obtained by exploiting a certain resource whose dynamics are governed by the fractional logistic equation. Due to the ...
SELF-SIMILARITY, SYMMETRIES AND ASYMPTOTIC BEHAVIOR IN MORREY SPACES FOR A FRACTIONAL WAVE EQUATION
(Khayyam Publ Co IncAthensEUA, 2012)
The fractional-nonlinear robotic manipulator: Modeling and dynamic simulations
(2012-12-01)
In this paper, we applied the Riemann-Liouville approach and the fractional Euler-Lagrange equations in order to obtain the fractional-order nonlinear dynamics equations of a two link robotic manipulator. The aformentioned ...
On the Initial-Boundary-Value Problem for the Time-Fractional Diffusion Equation on the Real Positive Semiaxis
(Hindawi Publishing Corporation, 2015-09)
We consider the time-fractional derivative in the Caputo sense of order α ∈ (0, 1). Taking into account the asymptotic behavior and the existence of bounds for the Mainardi and the Wright function in R+, two different ...
Mild Solutions To The Time Fractional Navier-stokes Equations In Rn
(Academic Press Inc., 2015)
Fractional derivative estimates in Gevrey spaces, global regularity and decay for solutions to semilinear equations in R-n
(Academic Press Inc Elsevier ScienceSan DiegoEUA, 2003)
On recent developments in the theory of abstract differential equations with fractional derivatives
(PERGAMON-ELSEVIER SCIENCE LTD, 2010)
This note is motivated from some recent papers treating the problem of the existence of a solution for abstract differential equations with fractional derivatives. We show that the existence results in [Agarwal et al. ...