A new method for searching the integral solution of system of Riemann–Liouville fractional differential equations with non-instantaneous impulses

• Published in: Journal of computational and applied mathematics Vol. 388; p. 113307
• Main Author: Zhang, Xian-Min
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.05.2021
• Subjects: Fractional differential equations; Impulsive fractional differential equations; Initial value problems; Non-instantaneous impulses; Nonuniqueness of solution; Impulsive fractional differential equations; Non-instantaneous impulses; Initial value problems; Fractional differential equations; Nonuniqueness of solution
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2020.113307

A new method is introduced for searching the integral solution to the system of non-instantaneous impulsive Riemann–Liouville fractional differential equations (NIRFrDE). For the system of NIRFrDE, its equivalent system is gained by applying some transformations, and its special integral solution and approximate integral solution are found out by considering fractional derivative from the whole interval and each local interval in the equivalent system, and then the error between the integral solution and approximate integral solution is computed to discover that the formula of integral solution is with some arbitrary constants. Finally, the main result is explained by computing the integral solution of a numerical example.