Existence and uniqueness results for Φ-Caputo implicit fractional pantograph differential equation with generalized anti-periodic boundary condition

Advances in Difference Equations

Thabet Abdeljawad¹  Fahd Jarad²  Piyachat Borisut³  Musa Ahmed Demba³  Idris Ahmed³  Poom Kumam⁴  Wiyada Kumam⁵ 

[1] Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia;Department of Medical Research, China Medical University Hospital, China Medical University, 40402, Taichung, Taiwan;Department of Computer Science and Information Engineering, Asia University Hospital, 40402, Taichung, Taiwan;Department of Mathematics, Faculty of Arts and Sciences, Çankaya University, 06790, Ankara, Turkey;Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, 10140, Bangkok, Thailand;Fixed Point Research Laboratory, Fixed Point Theory and Applications Research Group, Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, 10140, Bangkok, Thailand;Fixed Point Research Laboratory, Fixed Point Theory and Applications Research Group, Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, 10140, Bangkok, Thailand;Department of Medical Research, China Medical University Hospital, China Medical University, 40402, Taichung, Taiwan;Program in Applied Statistics, Department of Mathematics and Computer Science, Rajamangala University of Technology Thanyaburi, 12110, Thanyaburi, Pathumthani, Thailand;

关键词: Pantograph differential equation;    Φ-Caputo fractional derivative;    Anti-periodic condition;    34K20;    34K37;    32F18;   

DOI  :  10.1186/s13662-020-03008-x

来源: Springer

【 摘 要 】

The present paper describes the implicit fractional pantograph differential equation in the context of generalized fractional derivative and anti-periodic conditions. We formulated the Green’s function of the proposed problems. With the aid of a Green’s function, we obtain an analogous integral equation of the proposed problems and demonstrate the existence and uniqueness of solutions using the techniques of the Schaefer and Banach fixed point theorems. Besides, some special cases that show the proposed problems extend the current ones in the literature are presented. Finally, two examples were given as an application to illustrate the results obtained.

【 授权许可】

CC BY