arXiv subjects

Dušan Oberta

Publications and source records attributed to Dušan Oberta.

2 recordsLinked to original sources

arXiv2026

On the existence of solutions of dynamic equations on time scales in Banach spaces

In this paper we address the question of solvability of dynamic equations on time scales in Banach spaces. In particular, our main theorem extends the result for classical differential equations in Banach spaces of Banaś and Goebel (1980), to an arbitrary time scale. Central role is played by the axiomatic theory of measures of noncompactness and the newly introduced Kamke $Δ$-function. Also, we study countable systems of dynamic equations on time scales arising from semi-discretisation of parabolic partial dynamic equations.

math.FA↗

arXiv2025

On the existence of solutions of fractional differential equations in Banach spaces

Utilising the notion of measures of non-compactness and Kamke function of order $α$, we address the question of solvability of fractional differential equations in Banach spaces. In particular, we provide sufficient conditions ensuring the existence of a local solution. Our main existence theorem is then applied on countable systems of fractional differential equations arising from semi-discretisation of fractional PDEs with $p$-Laplacian.

math.FA↗