An iterative scheme for a class of fractional order perturbed differential equations

Abstract

This paper presents an existence and uniqueness theorem for a class of fractional order perturbed differential equations using modified quasilinearization method. A convergence analysis is accomplished not only using the monotone properties of the functions involved but also with a relaxation on these properties. The applicability of the proposed scheme is illustrated using examples assuring the uniqueness that the literature fails to achieve and the numerical simulation is done using the pseudo spectral method. © Springer Nature Singapore Pte Ltd 2019.