Representation of solutions of nonhomogeneous conformable fractional delay differential equations. (September 2021)

• Record Type: Journal Article
• Authors: Mahmudov, Nazim I.; Aydın, Mustafa
• Is Part Of: Chaos, solitons and fractals. Volume 150(2021)
• Publication Date: 2021-09
• Subjects: Conformable derivative -- Conformable delay perturbation -- Representation of solutions -- Existence -- Ulam-Hyers stability; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2021.111190
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: Linear and nonlinear time-delay equation with conformable fractional derivative is proposed. Conformable delay perturbation of matrix exponential function is defined for the first time. Solution of the equation is determined with the help of Conformable delay perturbation of matrix exponential function. Its existence, uniqueness and stability are proved via Banach Fixed Point Theorem and Ulam-Hyers Stability. Abstract: This paper is about the conformable fractional delay equations. We offer a conformable delay perturbation of matrix exponential function to give the representation of solutions for linear nonhomogeneous conformable fractional delay differential equations. Lastly, the existence and uniqueness of solutions and Ulam-Hyers stability of the equations are proved.