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1
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A note on some elementary properties and applications of certain operators to certain functions analytic in the unit disk

100%
Irmak H.
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
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2020
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tom 19
193-201
EN
This scientific note relates to introducing certain elementary operators defined in the unit disk in the complex plane, then determining various applications (specified by those operators) to certain analytic functions, and also revealing a number of possible implications of them.
2
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Set-valued fractional order differential equations in the space of summable functions

63%
Salem H.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2008
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tom 28
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nr 1
83-93
EN
In this paper, we study the existence of integrable solutions for the set-valued differential equation of fractional type $(D^{αₙ} - ∑_{i=1}^{n-1} a_i D^{α_i})x(t) ∈ F(t,x(φ(t)))$, a.e. on (0,1), $I^{1 - αₙ} x(0) = c$, αₙ ∈ (0,1), where F(t,·) is lower semicontinuous from ℝ into ℝ and F(·,·) is measurable. The corresponding single-valued problem will be considered first.
3
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Quadratic integral equations in reflexive Banach space

51%
Salem H.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2010
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tom 30
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nr 1
61-69
EN
This paper is devoted to proving the existence of weak solutions to some quadratic integral equations of fractional type in a reflexive Banach space relative to the weak topology. A special case will be considered.
4
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The use of a non-integer order PI controller with an active queue management mechanism

51%
Domański A., Domańska J., Czachórski T., Klamka J.
International Journal of Applied Mathematics and Computer Science
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2016
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tom 26
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nr 4
777-789
EN
In this paper the performance of a fractional order PI controller is compared with that of RED, a well-known active queue management (AQM) mechanism. The article uses fluid flow approximation and discrete-event simulation to investigate the influence of the AQM policy on the packet loss probability, the queue length and its variability. The impact of self-similar traffic is also considered.
5
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Recursive set membership estimation for output-error fractional models with unknown-but-bounded errors

51%
Amairi M.
International Journal of Applied Mathematics and Computer Science
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2016
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tom 26
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nr 3
543-553
EN
This paper presents a new formulation for set-membership parameter estimation of fractional systems. In such a context, the error between the measured data and the output model is supposed to be unknown but bounded with a priori known bounds. The bounded error is specified over measurement noise, rather than over an equation error, which is mainly motivated by experimental considerations. The proposed approach is based on the optimal bounding ellipsoid algorithm for linear output-error fractional models. A numerical example is presented to show effectiveness and discuss results.
6
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Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains

51%
Ostalczyk P.
International Journal of Applied Mathematics and Computer Science
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2012
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tom 22
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nr 3
533-538
EN
Two description forms of a linear fractional-order discrete system are considered. The first one is by a fractional-order difference equation, whereas the second by a fractional-order state-space equation. In relation to the two above-mentioned description forms, stability domains are evaluated. Several simulations of stable, marginally stable and unstable unit step responses of fractional-order systems due to different values of system parameters are presented.
7
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On a mixed-type integral equation and fractional-order functional differential equations

45%
El-Sayed A. M. A., Sherif N., Ibrahim I. A.
Commentationes Mathematicae
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2005
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tom 45
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nr 2
EN
In this paper we study the existence of solution of a nonlinear integral equation of (mixed type) Volterra-Fredholm type. As an application we prove the existence of solution of an initial value problem of fractional order in the space of Lebesgue integrable functions on the interval \([0, 1]\).
8
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An operational Haar wavelet method for solving fractional Volterra integral equations

45%
Saeedi H., Mollahasani N., Mohseni Moghadam M., Chuev G.
International Journal of Applied Mathematics and Computer Science
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2011
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tom 21
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nr 3
535-547
EN
A Haar wavelet operational matrix is applied to fractional integration, which has not been undertaken before. The Haar wavelet approximating method is used to reduce the fractional Volterra and Abel integral equations to a system of algebraic equations. A global error bound is estimated and some numerical examples with smooth, nonsmooth, and singular solutions are considered to demonstrate the validity and applicability of the developed method.
9
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Robust fractional adaptive control based on the strictly Positive Realness Condition

38%
Ladaci S., Charef A., Loiseau J.
International Journal of Applied Mathematics and Computer Science
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2009
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tom 19
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nr 1
69-76
EN
This paper presents a new approach to robust adaptive control, using fractional order systems as parallel feedforward in the adaptation loop. The problem is that adaptive control systems may diverge when confronted with finite sensor and actuator dynamics, or with parasitic disturbances. One of the classical robust adaptive control solutions to these problems makes use of parallel feedforward and simplified adaptive controllers based on the concept of positive realness. The proposed control scheme is based on the Almost Strictly Positive Realness (ASPR) property of the plant. We show that this condition implies also robust stability in the case of fractional order controllers. An application to Model Reference Adaptive Control (MRAC) with a fractional order adaptation rule is provided with an implementable algorithm. A simulation example of a SISO robust adaptive control system illustrates the advantages of the proposed method in the presence of disturbances and noise.
10
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Existence results for impulsive semilinear fractional differential inclusions with delay in Banach spaces

38%
Hammouche H., Guerbati K., Benchohra M., Abada N.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2013
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tom 33
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nr 2
149-170
EN
In this paper, we introduce a new concept of mild solution of some class of semilinear fractional differential inclusions of order 0 < α < 1. Also we establish an existence result when the multivalued function has convex values. The result is obtained upon the nonlinear alternative of Leray-Schauder type.
11
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Design of unknown input fractional-order observers for fractional-order systems

38%
N'Doye I., Darouach M., Voos H., Zasadzinski M.
International Journal of Applied Mathematics and Computer Science
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2013
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tom 23
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nr 3
491-500
EN
This paper considers a method of designing fractional-order observers for continuous-time linear fractional-order systems with unknown inputs. Conditions for the existence of these observers are given. Sufficient conditions for the asymptotical stability of fractional-order observer errors with the fractional order α satisfying 0 < α < 2 are derived in terms of linear matrix inequalities. Two numerical examples are given to demonstrate the applicability of the proposed approach, where the fractional order α belongs to 1 ≤ α < 2 and 0 < α ≤ 1, respectively. A stability analysis of the fractional-order error system is made and it is shown that the fractional-order observers are as stable as their integer order counterpart and guarantee better convergence of the estimation error.
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