Analytical analysis of fractional-order sequential hybrid system with numerical application

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.

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Coupled system of three sequential Caputo fractional differential equations: Existence and stability analysis

“…The fractional calculus plays a significant role in differential equations and applied sciences. Several researchers have studied structures of differential equations and systems using fractional calculus; for instance, see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Many important and interesting areas concerning research for fractional differential equations and fractional systems are devoted to the existence theory and stability analysis of the solutions.…”

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