Journal
CHAOS SOLITONS & FRACTALS
Volume 162, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.chaos.2022.112511
Keywords
Virus AH1N1/09; Fractal-fractional operator; Adams-Bashforth; Kumar-Erturk method; Stability
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In this paper, a new model of AH1N1/09 influenza virus is formulated based on the four classes of susceptible, exposed, infectious and recovered people. The model is investigated using fractal-fractional operators and power law type kernels. The existence of solution is studied using special mappings and the Leray-Schauder theorem. The stability criteria is explored and numerical solutions are approximated using the Adams-Bashforth scheme.
In this paper, we formulate a new model of a particular type of influenza virus called AH1N1/09 in the framework of the four classes consisting of susceptible, exposed, infectious and recovered people. For the first time, we here investigate this model with the help of the advanced operators entitled the fractal-fractional operators with two fractal and fractional orders via the power law type kernels. The existence of solution for the mentioned fractal-fractional model of AH1N1/09 is studied by some special mappings such as ?-psi-contractions and ?-admissibles. The Leray-Schauder theorem is also applied for this aim. After investigating the stability criteria in four versions, to approximate the desired numerical solutions, we implement Adams-Bashforth (AB) scheme and simulate the graphs for different data on the fractal and fractional orders. Lastly, we convert our fractal-fractional AH1N1/09 model into a fractional model via the generalized Liouville-Caputo-type (GLC-type) operators and then, we simulate new graphs caused by the new numerical scheme called Kumar-Erturk method.
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