Study of fractional order pantograph type impulsive antiperiodic boundary value problem

Advances in Difference Equations

Aziz Khan¹  Thabet Abdeljawad²  Hasib Khan³  Arshad Ali⁴  Kamal Shah⁴ 

[1] Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia;Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia;Department of Medical Research, China Medical University, 40402, Taichung, Taiwan;Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan;Department of Mathematics, Shaheed BB University, Dir Uppr, Khyber Pakhtunkhwa, Pakistan;Department of Mathematics, University of Malakand, Dir(L), Khyber Pakhtunkhwa, Pakistan;

关键词: Delay differential equation;    Impulsive conditions;    Schaefer’s fixed point theorem;    Hyers–Ulam stability;   

DOI  :  10.1186/s13662-020-03032-x

来源: Springer

【 摘 要 】

In this paper, we study existence and stability results of an anti-periodic boundary value problem of nonlinear delay (pantograph) type implicit fractional differential equations with impulsive conditions. Using Schaefer’s fixed point theorem and Banach’s fixed point theorem, we have established results of at least one solution and uniqueness. Also, using the Hyers–Ulam concept, we have derived various kinds of Ulam stability results for the considered problem. Finally, we have applied our obtained results to a numerical problem.

【 授权许可】

CC BY