Existence of anti-periodic boundary value problem for a class of nonlinear Hilfer fractional Langevin equations
by Lu Deng, Huiwen Wang, and Fang Li
School of Mathematics, Yunnan Normal University, Kunming, 650500, P. R. China
Received on March 24, 2026, revised on April 10, 2026
Accepted on April 11, 2026
Communicated by Gaston M. N'Guérékata
| Abstract. In this work, we study anti-periodic boundary value problem of Hilfer Langevin equations. Applying generalized Mittag-Leffler functions, we prove the equivalence between the boundary value problem under consideration and an integral equation. Moreover, we obtain existence of solutions for the above boundary value problem in a weighted space. An example is given to demonstrate the consistency with our theoretical results. | |
| Keywords: | Fractional Langevin equation, Hilfer fractional derivative, anti-periodic problem, weighted space. |
| 2010 Mathematics Subject Classification: 26A33, 33E12, 34B15. | |
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