Problem on piecewise Caputo-Fabrizio fractional delay differential equation under anti-periodic boundary conditions. (1st March 2023)

• Record Type: Journal Article
• Authors: Filali, D; Ali, Arshad; Ali, Zeeshan; Akram, M; Dilshad, M; Agarwal, Praveen
• Is Part Of: Physica scripta. Volume 98:Number 3(2023)
• Publication Date: 2023-03-01
• Subjects: piecewise derivative -- caputo fabrizio derivative -- proportional delay -- stability results; Physics -- Periodicals; 530.05
• DOI: 10.1088/1402-4896/acb6c4
• Languages: English
• ISSNs: 0031-8949

Abstract

Abstract: This manuscript considers a class of piecewise differential equations (DEs) modeled with the Caputo-Fabrizio differential operator. The proposed problem involves a proportional delay term and is equipped with anti-periodic boundary conditions. The piecewise derivative can be applied to model many complex nature real-world problems that show a multi-step behavior. The existence theory and Hyer-Ulam (HU) stability results are studied for the proposed problem via fixed point techniques such as Banach contraction theorem, Schauder's fixed point theorem and Arzelá Ascoli theorem. A numerical problem is presented as an example to see the validity and effectiveness of the applied concept.