Baleanu, D.Makhlouf, Abdellatif BenNagy, A. M.Boucenna, Djalal02.02. Matematik02. Fen-Edebiyat Fakültesi01. Çankaya Üniversitesi2022-03-172025-09-182022-03-172025-09-182021Boucenna, Djalal...et al. (2021). "Analysis and numerical solution of the generalized proportional fractional Cauchy problem", Applied Numerical Mathematics, Vol. 167, pp. 173-186.0168-92741873-5460https://doi.org/10.1016/j.apnum.2021.04.015https://hdl.handle.net/123456789/12697Nagy, A. M./0000-0003-4335-6990; Ben Makhlouf, Abdellatif/0000-0001-7142-7026In 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. (C) 2021 IMACS. Published by Elsevier reserved.eninfo:eu-repo/semantics/closedAccessFractional Differential EquationsGeneralized Proportional Fractional DerivativeArticle10.1016/j.apnum.2021.04.0152-s2.0-85105586935