Existence of solutions for nonlinear problems involving mixed fractional derivatives with p(x)-Laplacian operator

In this article, a functional boundary value problem involving mixed fractional derivatives with p(x)-Laplacian operator is investigated. Based on the fixed point theorems and Mawhin’s coincidence theory’s extension theory, some existence theorems are obtained in the case of non-resonance and the case of resonance. Some examples are supplied to verify our main results.

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Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).