We propose a Grünwald–Letnikov-type derivative using a continuous positive function T.

This function generalizes some conformable and nonconformable derivative kernels known from the literature. First, we obtain basic properties, such as the Leibniz rule and the index law for this fractional derivative. We also prove integral representations and show that this derivative does not, in general, map periodic functions onto periodic functions with the same period. Finally, we conclude that…

We have just published a paper entitled “Borel–Pompeiu Formula for a Higher-Order Lamé–Navier System in the Plane.” We establish a Borel–Pompeiu integral representation formula for a higher-order Lamé–Navier system of order p in the plane. Our approach is based on the construction of suitable fundamental kernels adapted to the higher-order structure. In particular, the classical Lamé–Navier system is recovered when p = 1, showing that the present results provide a natural higher-order…

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In this paper, we address the question of whether a Hölder continuous function defined on a Lyapunov surface can be decomposed as the sum of the two boundary traces of a sectionally (alpha,beta)-monogenic function. Our main tool consists of the Hardy projections associated with a singular integral operator arising in Clifford analysis, which turns out to be an involutive…