Mathematical Methods in the Applied Sciences, vol.45, no.7, pp.3417-3425, 2022 (Journal Indexed in SCI Expanded)
Article / Article
Mathematical Methods in the Applied Sciences
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Caputo fractional derivative, existence and uniqueness, fixed point, Langevin equation, Ulam-Hyers stability, INTEGRAL-EQUATIONS, UNIQUENESS, ORDERS
© 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.