Analysis of the spread of Hookworm infection with Caputo-Fabrizio fractional derivative

Yıl 2022, Cilt: 7 Sayı: 1, 43 - 52, 30.04.2022

Esin İlhan

Öz

This research study provides a mathematical analysis for the spread of Hookworm infection
model. Firstly, the proposed disease model is extended by means of the Caputo-Fabrizio fractional derivative. Then, existence and uniqueness of the solution is presented for the fractional-type Hookworm infection
model with the help of the fixed-point theorem. Theoretical results of the model under consideration show
the advantages of the fractional differential operators.

Anahtar Kelimeler

Modeling, Fractional derivative, Caputo-Fabrizio

Kaynakça

• [1] Ismael HF, Atas SS, Bulut H, Osman MS. Analytical solutions to the M-derivative resonant Davey–Stewartson equations. Modern Physics Letters B. 2021 Oct 30;35(30):2150455.
• [2] Ismael HF, Bulut H, Baskonus HM, Gao W. Dynamical behaviors to the coupled Schrodinger-Boussinesq system with the beta ¨ derivative. AIMS Mathematics. 2021;6(7):7909-28.
• [3] Gao W, Ismael HF, Mohammed SA, Baskonus HM, Bulut H. Complex and real optical soliton properties of the paraxial non-linear Schrodinger equation in Kerr media with M-fractional. Frontiers in Physics. 2019 Nov 21;7:197.
• [4] Caputo M, Fabrizio M. A new definition of fractional derivative without singular kernel. Progr Fract Differ Appl 1 (2): 73–85.
• [5] Mustapha UT, Qureshi S, Yusuf A, Hincal E. Fractional modeling for the spread of Hookworm infection under Caputo operator. Chaos, Solitons & Fractals. 2020 Aug 1;137:109878.
• [6] Losada J, Nieto JJ. Properties of a new fractional derivative without singular kernel. Progr. Fract. Differ. Appl. 2015 Apr;1(2):87-92.
• [7] Caputo M. Linear models of dissipation whose Q is almost frequency independent—II. Geophysical Journal International. 1967 Nov 1;13(5):529-39.
• [8] Podlubny I. Fractional differential equations, mathematics in science and engineering. San Diego: Academic Press, 1999.
• [9] Bulut H, Ilhan E. Fractional vector-borne disease model with lifelong immunity under Caputo operator. Physica Scripta. 2021 May 20;96(8):084006