Generalized fractional differential equation with Hilfer fractional derivatives

Bayan Bekbolat, Sultan Kimatov, Akniyet Mussakhan, Niyaz Tokmagambetov

2025

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DOI 10.70474/ypdts083
Data confidence 85 high
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Abstract

In this paper, we investigate the solvability of fractional differential equations involving the Hilfer fractional derivative. This derivative serves as an interpolation between the Caputo and Riemann–Liouville derivatives, depending on the value of a parameter. Our study extends previous results obtained by G. Bozkurt, D. Albayrak, N. Dernekin (2019), who considered similar equations with the Riemann–Liouville derivative, and earlier work by S.-D. Lin and C.-H. Lu (2013) involving the Caputo derivative. By applying the Laplace transform method, we establish the existence result for the proposed problem.