Mathematica Moravica, Vol. 26, No. 2 (2022)

N. Hadj Taieb, M.A. Hammami, M. Hammi
On the global uniform stability analysis of non-autonomous dynamical systems: A survey
Mathematica Moravica, Vol. 26, No. 2 (2022), 1–48.
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Abstract. In this survey, we introduce the notion of stability of time varying nonlinear systems. In particular we investigate the notion of global practical exponential stability for non-autonomous systems. The proposed approach for stability analysis is based on the determination of the bounds of perturbations that characterize the asymptotic convergence of the solutions to a closed ball centered at the origin.
Keywords. Lyapunov theory, Perturbed systems, Practical stability.

Mohammed Benyoub, Kacem Belghaba
Anti-periodic boundary value problems for Caputo-Fabrizio fractional impulsive differential equations
Mathematica Moravica, Vol. 26, No. 2 (2022), 49–62.
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Abstract. In this paper, we shall discuss the existence and uniqueness of solutions for a nonlinear anti-periodic boundary value problem for fractional impulsive differential equations involving a Caputo-Fabrizio fractional derivative of order $r\in(0,1)$. Our results are based on some fixed point theorem, nonlinear alternative of Leray-Schauder type and coupled lower and upper solutions.
Keywords. Fractional differential equation, Caputo-Fabrizio integral of fractional order, Caputo-Fabrizio fractional derivatives, Anti-periodic boundary value problem, Fixed point, Lower and upper solutions, coupled lower and upper solutions.

Şenol Dost
Weak preopen sets and weak bicontinuity in texture spaces
Mathematica Moravica, Vol. 26, No. 2 (2022), 63–71.
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Abstract. The aim of this paper is introduce and study the notion of weak preopen sets and weak prebicontinuity on weak structures in texture spaces. It is presented some characterizations of weak prebicontinuity, and a link is given between weak spaces and weak structure on discrete texture spaces.
Keywords. Texture, Fuzzy set, Weak structure, Weak preopen set, Weak prebicontinuity.

Süleyman Çetinkaya, Ali Demir
Effects of the ARA transform method for time fractional problems
Mathematica Moravica, Vol. 26, No. 2 (2022), 73–84.
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Abstract. The aim of this study is to establish the solutions of time fractional mathematical problems with the aid of new integral transforms called the ARA transform. The fractional derivative is taken in the sense of Liouville-Caputo derivative. The fractional partial differential equations are reduced into ordinary differential equations. Later solving this fractional equation and applying inverse the ARA transform, the solution is acquired. The implementation of this transform for fractional differential equations is very similar to the implementation of the Laplace transform. However, the ARA transform allows us to take the integral transform of some functions for which we can not take the Laplace transform. The illustrated examples justify that the implementation and efficiency of this method are better than any other integral transforms to tackle time fractional differential equations (TFDEs).
Keywords. Liouville-Caputo fractional derivative, time fractional partial differential equation, ARA integral transform.