Study of a nonlinear multi-terms boundary value problem of fractional pantograph differential equations

Advances in Difference Equations

article

Bahar Ali Khan, Muhammad¹  Abdeljawad, Thabet²  Shah, Kamal⁵  Ali, Gohar¹  Khan, Hasib⁶  Khan, Aziz² 

[1] Department of Mathematics, Islamia College University;Department of Mathematics and General Sciences, Prince Sultan University;Department of Medical Research, China Medical University;Department of Computer Science and Information Engineering, Asia University;Department of Mathematics, University of Malakand;Department of Mathematics, Shaheed Benazir Bhutto University

关键词: Multi-term FODEs;    Proportional delay;    Stability theory of Ulam;   

DOI  :  10.1186/s13662-021-03313-z

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this research work, a class of multi-term fractional pantograph differential equations (FODEs) subject to antiperiodic boundary conditions (APBCs) is considered. The ensuing problem involves proportional type delay terms and constitutes a subclass of delay differential equations known as pantograph. On using fixed point theorems due to Banach and Schaefer, some sufficient conditions are developed for the existence and uniqueness of the solution to the problem under investigation. Furthermore, due to the significance of stability analysis from a numerical and optimization point of view Ulam type stability and its various forms are studied. Here we mention different forms of stability: Hyers–Ulam (HU), generalized Hyers–Ulam (GHU), Hyers–Ulam Rassias (HUR) and generalized Hyers–Ulam–Rassias (GHUR). After the demonstration of our results, some pertinent examples are given.

【 授权许可】

CC BY