An existence result for a periodic boundary value problem of fractional semilinear differential equations in a Banach space
Mikhail A. Kamenskii, Garik Petrosyan, Ching‐Feng Wen, M Afanasova, Y Liou, V Obukhoskii, G Petrosyan, M Afanasova, G Petrosyan, J Appell, B Lopez, K Sadarangani, I Benedetti, V Obukhovskii, V Taddei, F Mainardi, M Kamenskii, V Obukhovskii, G Petrosyan, J Yao, M Kamenskii, V Obukhovskii, G Petrosyan, J Yao, M Kamenskii, V Obukhovskii, G Petrosyan, J Yao, M Kamenskii, V Obukhovskii, G Petrosyan, J Yao, Z Hong, L Jiao, D Kim, T Ke, N Loi, V Obukhovskii, T Ke, V Obukhovskii, N Wong, J Yao, G Petrosyan, M Afanasova, Z Zhang, B Liu, M Abbas, M Belmekki, J Nieto, R Rodriguez-Lopez, M Belmekki, J Nieto, R Rodiguez-Lopez, Z Bai, H Lu
Abstract
We consider the periodic boundary value problem for a semilinear differential equation of a fractional order q (1, 2) in a Banach space. We prove auxiliary statements about fractional derivatives. To solve this problem, we introduce the integral operator whose fixed points coincide with mild solutions of our problem. An existence result is established.