A study on fractional differential equations using the fractional Fourier transform
Porpattama Hammachukiattikul, A. Mohanapriya, Anumanthappa Ganesh, Grienggrai Rajchakit, Vediyappan Govindan, Nallappan Gunasekaran, Chee Peng Lim
Abstract
Abstract This study aims to use the fractional Fourier transform for analyzing various types of Hyers–Ulam stability pertaining to the linear fractional order differential equation with Atangana and Baleanu fractional derivative. Specifically, we establish the Hyers–Ulam–Rassias stability results and examine their existence and uniqueness for solving nonlinear problems. Simulation examples are presented to validate the results.
Topics & Concepts
MathematicsFractional calculusUniquenessStability (learning theory)Ordinary differential equationPartial differential equationFourier transformNonlinear systemApplied mathematicsMathematical analysisDifferential equationComputer scienceQuantum mechanicsPhysicsMachine learningFractional Differential Equations SolutionsFunctional Equations Stability ResultsNonlinear Differential Equations Analysis