Abstract
We investigate a general sequential hybrid class of fractional differential equations in the Caputo and Atangana–Baleanu fractional senses of derivatives. We consider the existence and uniqueness of solutions and the Hyers–Ulam (H-U) stability for a general class. We use the Banach and Leray–Schauder alternative theorems for the existence criteria. With the help of nonnegative Green’s functions, the fractional-order class is turned into m-equivalent integral forms. As an application of our problem, a fractional-order smoking model in terms of the Atangana–Baleanu derivative is presented as a particular case.
Highlights
Mathematical modeling of dynamical systems and their numerical simulations are widely studied in science and engineering
We investigate a general sequential hybrid class of fractional differential equations in the Caputo and Atangana–Baleanu fractional senses of derivatives
The general classes of the fractional-order differential equations (FDEs) were considered by experts. This area is still open for sequential fractional differential equations, hybrid FDEs, mixed fractional functional equations, and many more
Summary
Mathematical modeling of dynamical systems and their numerical simulations are widely studied in science and engineering. Abstract We investigate a general sequential hybrid class of fractional differential equations in the Caputo and Atangana–Baleanu fractional senses of derivatives. With the help of nonnegative Green’s functions, the fractional-order class is turned into m-equivalent integral forms. As an application of our problem, a fractional-order smoking model in terms of the Atangana–Baleanu derivative is presented as a particular case.
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