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

Dušan Oberta

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arXiv · 2511.01944

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

Dušan Oberta

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Abstract

Utilising the notion of measures of non-compactness and Kamke function of order $\alpha$, 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.

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Dušan Oberta. 2025-11-03. On the existence of solutions of fractional differential equations in Banach spaces. https://arxiv.org/abs/2511.01944

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