A Novel Investigation of Non-Periodic Snap <i>BVP</i> in the <inline-formula><math display="inline"><semantics><mi mathvariant="double-struck">G</mi></semantics></math></inline-formula>-Caputo Sense

Abstract

In the present paper, we consider a nonlinear fractional snap model with respect to a G-Caputo derivative and subject to non-periodic boundary conditions. Some qualitative analysis of the solution, such as existence and uniqueness, are investigated in view of fixed-point theorems. Moreover, the stabilities of Ulam–Hyers and Ulam–Hyers–Rassias criterions are considered and investigated. Some numerical simulations were performed using MATLAB for understanding the theoretical results. All results in this work play an important role in understanding ocean engineering phenomena due to the huge applicability of jerk and snap in seakeeping, ride comfort, and shock response spectrum.

Keywords

• snap problem
• \({\mathbb{G}}\)-Caputo fractional differential equation
• boundary value problem
• Ulam–Hyers–Rassias stability