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

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–Schaude...

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Bibliographic Details
Published inAdvances in continuous and discrete models Vol. 2022; no. 1
Main Authors Khan, Aziz, Khan, Zareen A., Abdeljawad, Thabet, Khan, Hasib
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 02.02.2022
Springer Nature B.V
Subjects
Analysis
Difference and Functional Equations
Differential equations
Dynamical systems
Existence theorems
Functional Analysis
Green's functions
Hybrid systems
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Science
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Summary: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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ISSN:2731-4235
1687-1839
2731-4235
1687-1847
DOI:10.1186/s13662-022-03685-w