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DEVELİ F.
Mathematical Methods in the Applied Sciences, vol.45, no.7, pp.3417-3425, 2022 (SCI-Expanded)
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Publication Type:
Article / Article
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Volume:
45
Issue:
7
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Publication Date:
2022
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Doi Number:
10.1002/mma.7987
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Journal Name:
Mathematical Methods in the Applied Sciences
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Journal Indexes:
Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
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Page Numbers:
pp.3417-3425
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Keywords:
Caputo fractional derivative, existence and uniqueness, fixed point, Langevin equation, Ulam-Hyers stability, INTEGRAL-EQUATIONS, UNIQUENESS
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Yıldız Technical University Affiliated:
Yes
Abstract
© 2021 John Wiley & Sons, Ltd.In this paper, we give the existence and uniqueness result for the fractional order Langevin equation with modified argument by using the Bielecki norm. After, we consider a special form of this equation (delayed form) and then apply Burton's method to this special form to prove that there is a unique solution under weaker conditions than the other result. Further, we derive the Ulam–Hyers stability for this equation. Finally, two examples are given to illustrate our main results.