عنوان	On the fractional hybrid Sturm-Liouville and Langevin differential equations and inclusions in the frame of $\uppsi$-Hilfer operator
نوع پژوهش	مقاله چاپ‌شده در مجلات علمی
کلیدواژه‌ها	Inclusion; $\uppsi$--Hilfer fractional derivative; existence and uniqueness; nonlinear analysis; Ulam stability
چکیده	In this investigation, we explore the existence and uniqueness of solutions for fractional hybrid differential equations and inclusions of Langevin and Sturm-Liouville within the sense of the $\uppsi$--Hilfer fractional derivatives. We characterize an unused operator based on the integral solution of the given boundary value inclusion problem, and after that we utilize the presumptions of Dhage's fixed point for the operator within the hybrid case. The theorem is connected for the boundary value problem in the single-valued case uniqueness of solution which is decided by utilizing Banach's contraction mapping rule. Moreover, the stability analysis within the Ulam-Hyers sense of a given system is considered. At last, illustrations are advertised to guarantee the legitimacy of our obtained results.
پژوهشگران	عبدالطیف بوتیارا (نفر اول)، محمد کا ام کابار (نفر دوم)، محمداسماعیل سامعی (نفر سوم)