Analysis and numerical solution of the generalized proportional fractional Cauchy problem

• DOI: 10.1016/j.apnum.2021.04.015
• Publication Date: 2021-05-04T15:48:30Z
• Authors: Djalal Boucenna; D. Baleanu; Abdellatif Ben Ma...; A.M. Nagy
• Keywords: Cauchy's convergence test; Derivative (finance)

Abstract In this paper, we explore the existence and uniqueness theorem for a problem of the fractional Cauchy form, with dependence on the generalized proportional Caputo derivative. Furthermore, a new numerical technique is presented based on a decomposition formula for the generalized proportional Caputo derivative. Convergence analysis of the proposed technique is proved. Finally, numerical results are obtained to confirm the validity of the proposed method.