Open AccessOn new computations of the fractional epidemic childhood disease model pertaining to the generalized fractional derivative with nonsingular kernel
Author(s) -
Saima Rashid,
AUTHOR_ID,
Fahd Jarad,
F. S. Bayones,
AUTHOR_ID,
AUTHOR_ID,
AUTHOR_ID
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022254
Subject(s) - invertible matrix , uniqueness , fractional calculus , mathematics , kernel (algebra) , stability (learning theory) , adomian decomposition method , decomposition , derivative (finance) , decomposition method (queueing theory) , calculus (dental) , pure mathematics , computer science , mathematical analysis , medicine , statistics , differential equation , ecology , dentistry , machine learning , financial economics , economics , biology
The present research investigates the Susceptible-Infected-Recovered (SIR) epidemic model of childhood diseases and its complications with the Atangana-Baleanu fractional derivative operator in the Caputo sense (ABC). With the aid of the Elzaki Adomian decomposition method (EADM), the approximate solutions of the aforesaid model are discussed by exerting the Adomian decomposition method. By employing the fixed point postulates and the Picard–Lindelöf approach, the stability, existence, and uniqueness consequences of the model are demonstrated. Furthermore, we illustrate the essential hypothesis for disease control in order to find the role of unaware infectives in the spread of childhood diseases. Besides that, simulation results and graphical illustrations are presented for various fractional-orders. A comparison analysis is shown with the previous findings. It is hoped that ABC fractional derivative and the projected algorithm will provide new venues in futuristic studies to manipulate and analyze several epidemiological models.