Analysis of Implicit Type Nonlinear Dynamical Problem of Impulsive Fractional Differential Equations. (12th February 2018)

• Record Type: Journal Article
• Authors: Ahmad, Naveed; Ali, Zeeshan; Shah, Kamal; Zada, Akbar; ur Rahman, Ghaus
• Other Names: Agop Maricel Academic Editor.
• Is Part Of: Complexity. Volume 2018(2018)
• Publication Date: 2018-02-12
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2018/6423974
• Languages: English
• ISSNs: 1076-2787

Abstract

Abstract : We study the existence, uniqueness, and various kinds of Ulam–Hyers stability of the solutions to a nonlinear implicit type dynamical problem of impulsive fractional differential equations with nonlocal boundary conditions involving Caputo derivative. We develop conditions for uniqueness and existence by using the classical fixed point theorems such as Banach fixed point theorem and Krasnoselskii's fixed point theorem. For stability, we utilized classical functional analysis. Also, an example is given to demonstrate our main theoretical results.