Darzi, RahmatAgheli, BahramBaleanu, Dumitru02.02. Matematik02. Fen-Edebiyat Fakültesi01. Çankaya Üniversitesi2021-01-292025-09-182021-01-292025-09-182020Baleanu, Dumitru; Darzi, Rahmat; Agheli, Bahram (2020). "Existence Results for Langevin Equation Involving Atangana-Baleanu Fractional Operators", Mathematics, Vol. 8, No. 3.2227-7390https://doi.org/10.3390/math8030408https://hdl.handle.net/123456789/12079Agheli, Bahram/0000-0003-2084-4158A new form of nonlinear Langevin equation (NLE), featuring two derivatives of non-integer orders, is studied in this research. An existence conclusion due to the nonlinear alternative of Leray-Schauder type (LSN) for the solution is offered first and, following that, the uniqueness of solution using Banach contraction principle (BCP) is demonstrated. Eventually, the derivatives of non-integer orders are elaborated in Atangana-Baleanu sense.eninfo:eu-repo/semantics/openAccessAtangana-Baleanu Fractional DerivativeLangevin EquationLeray-Schauder NonlinearExistence Results26A3347E05Article10.3390/math80304082-s2.0-85082407916