@article{Khan2023, 
author = {Hasib Khan and Jehad Alzabut and J.F. Gómez-Aguilar and Praveen Agarwal},
title = {Piecewise mABC fractional derivative with an application},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {10},
pages = {24345-24366},
keywords = {picewise modified ABC derivative, tuberculosis, solution existence, Hyres-Ulam stability, numerical simulations},
url = {https://www.sciopen.com/article/10.3934/math.20231241},
doi = {10.3934/math.20231241},
abstract = {In this study, we give the notion of a piecewise modified Atangana-Baleanu-Caputo (mABC) fractional derivative and apply it to a tuberculosis model. This novel operator is a combination of classical derivative and the recently developed modified Atangana-Baleanu operator in the Caputo's sense. For this combination, we have considered the splitting of an interval    [  0  ,      t    2    ] for        t    2    ∈            R        +  , such that, the classical derivative is applied in the first portion    [  0  ,      t    1    ] while the second differential operator is applied in the interval    [      t    1    ,      t    2    ]. As a result, we obtained the piecewise mABC operator. Its corresponding integral is also given accordingly. This new operator is then applied to a tuberculosis model for the study of crossover behavior. The existence and stability of solutions are investigated for the nonlinear piecewise modified ABC tuberculosis model. A numerical scheme for the simulations is presented with the help of Lagrange's interpolation polynomial is then applied to the available data.}
}