This research demonstrates solution existence and stability in boundary value problems using hybrid fractional derivatives, suggesting new analytical methods.
In this paper, we study some existence and stability results related to the boundary value problem involving the Atangana–Baleanu–Caputo hybrid fractional derivative. More precisely, we transform the studied problem to an equivalent integral equation, and after that, by applying appropriate fixed-point theorems and using suitable conditions, we prove the existence of solutions. Furthermore, we derive sufficient conditions that guarantee the stability in the sense of Hyers–Ulam. To support the theoretical findings, we present illustrative examples along with numerical simulations.
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Almaghamsi et al. (2026) studied this question.
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