On a novel fractional Caputo-derivative Orlicz space

2024/08/03 by Ayoub, Kasmi, Houssine, Azroul El, Mohammed Shimi +1 · 1 citation
Mathematics · #Approximation Theory and Sequence Spaces #Advanced Harmonic Analysis Research #Advanced Banach Space Theory

paper · pdf · doi:10.48550/arxiv.2408.01842

Abstract

In this work, we aim to explore whether a novel type of fractional space can be defined using Orlicz spaces and fractional calculus. This inquiry is fruitful, as extending classical results to new contexts can lead to a better and deeper understanding of those classical results. Our main objective is to introduce a new fractional Caputo-derivative Orlicz space, denoted by O^α,G(Λ, ℝ) . We are interested in several qualitative properties of this space, such as reflexivity, completeness, and separability. Additionally, we establish a continuous embedding results of this space into a suitable Orlicz space and the space of continuous functions. As an application, we use the mountain-pass theorem (MPT) to ensure the existence of a nontrivial weak solution for a new class of fractional-type problems in Orlicz space.

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• Fundamental Properties and Embedding Results in a Novel (Φ_x, ψ)-Fractional Musielak Space with an Application to Nonlocal BVP

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