Mathematica Moravica, Vol. 28, No. 2 (2024)

Editorial Board
IN MEMORIAM: Prof. dr Mališa Žižović (1948–2024)
Mathematica Moravica, Vol. 28, No. 2 (2024).
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Subhadip Roy, Parbati Saha, Binayak S. Choudhury, Rajendra Pant
Some coupled fixed point results for multi-valued nonlinear contractions in metric spaces using $w$-distance
Mathematica Moravica, Vol. 28, No. 2 (2024), 1–16.
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Abstract. This study employs contractive criteria related to $w$-distances to design and address a non-linear multivalued fixed point problem. The results presented in this study are substantiated by the inclusion of three illustrative examples. In this work, a dedicated portion is allocated to the examination of the use of $w$-distances. Specifically, it explores how the utilization of $w$-distances in the current context expands upon the findings derived from metric distances.
Keywords. Multi-valued contraction, $w$-distance, ceiling distance, coupled fixed point.

Tatjana Mirković, Tatjana Bajić
Opial inequalities for a conformable $\Delta$-fractional calculus on time scales
Mathematica Moravica, Vol. 28, No. 2 (2024), 17–32.
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Abstract. In this paper, an Opial-type inequality is introduced on time scale for a conformal $\Delta$-fractional differentiable function of order $\alpha$, $\alpha\in (0,1]$. In the case where the certain weight functions are included, one generalization of the Opial inequality is proved using conformal $\Delta$-fractional calculus on time scales. Moreover, for $n$ times conformal $\Delta$-fractional differentiable function on time scale, $n \in\mathbb N$, an Opial inequality is obtained. In particular, through examples, the main results from the paper are compared with classical ones on generalized time scales. At the end of the paper, we indicate possible applications of the obtained Opial-type inequalities in the consideration of stochastic dynamical equations where conformal $\Delta$-fractional calculus on time scales is included, which requires further research.
Keywords. Opial inequality, conformable $\Delta$-fractional differentiable function, time scale.

Adeyanju, A.A., Fabelurin, O.O., Akinbo, G., Aduroja, O.O., Ademola, A.T., Ogundiran, M.O., Ogundare, B.S., Adesina, O.A.
Criteria for the asymptotic behaviour of solutions to certain third-order nonlinear differential equations
Mathematica Moravica, Vol. 28, No. 2 (2024), 33–44.
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Abstract. We investigate and provide sufficient criteria for ultimate boundedness of solutions as well as the asymptotic stability of the trivial solution to certain nonlinear differential equation of order three. Using the Lyapunov second method and the Yoshizawa limit point approach, we establish our results. The equation considered is new and more general. Hence, our results are new, generalized and improved on some earlier established results. In order to verify the correctness of our obtained results, a numerical example is provided with the trajectories of the solutions.
Keywords. Stability, boundedness, asymptotic behaviour, Lyapunov function.