On a generalized Caputo for Langevin fractional differential equations in Banach spaces

	On a generalized Caputo for Langevin fractional differential equations in Banach spaces
International Journal of Nonlinear Analysis and Applications
مقاله 1، دوره 14، شماره 12، اسفند 2023، صفحه 1-12 اصل مقاله (423.95 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.29384.4145
نویسنده
Abdelatif Boutiara^*
Laboratory of Mathematics And Applied Sciences, University of Ghardaia, 47000 Ghardaia. Algeria
چکیده
In this research article, we study the existence, uniqueness and Ulam-Hyers stability of solutions in connection to the generalized Caputo Langevin fractional differential equations in Banach Space. The existence, uniqueness, and stability in the sense of Ulam are established for the proposed system. Our approach is based on the technique of measure of noncompactness combined with the Monch fixed point theorem, the implementation Banach contraction principle fixed point theorem. Moreover, the Ulam--Hyers stability is discussed by utilizing the Urs's. Lastly, we deliver an example to check the efficiency and accuracy of the proposed methods.
کلیدواژه‌ها
Fractional Langevin equation؛ $\psi$-Caputo؛ Ulam-Hyers stability؛ Kuratowski measures of noncompactness؛ fixed point theorems؛ Banach space
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