Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 16 1 2024 07 01 On the hybrid fractional semilinear evolution equations 307 318 8485 10.22075/ijnaa.2023.28018.3781 EN Samira Zerbib Laboratory LMACS, Sultan Moulay Slimane University, BP 523, Beni Mellal, 23000, Morocco Khalid Hilal Laboratory LMACS, Sultan Moulay Slimane University, BP 523, Beni Mellal, 23000, Morocco Ahmed Kajouni Laboratory LMACS, Sultan Moulay Slimane University, BP 523, Beni Mellal, 23000, Morocco Journal Article 2022 08 05 In this manuscript, we study the existence of mild solutions to initial value problems for hybrid fractional semi-linear evolution equations. On the other hand, we prove four different types of Ulam-Hyers stability results for mild solutions. The existence of mild solutions is proved by the Dhage fixed point theorem. Finally, an example is given to illustrate our results. Hybrid fractional evolution equation Mild solution Ulam-Hyers stability Fixed point theorem https://ijnaa.semnan.ac.ir/article_8485_756c6dcd65feb9755c40a1da3dd33cb2.pdf