Existence and uniqueness of solutions of initial value problems for nonlinear langevin equation involving two fractional orders

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• 作者：Tao Yu ; Ke Deng ; Maokang Luo
• 关键词：Fractional Langevin equation ; Caputo fractional derivative ; Initial value problem ; Existence and uniqueness ; Fixed point
• 刊名：Communications in Nonlinear Science and Numerical Simulation
• 出版年：June, 2014
• 年：2014
• 卷：19
• 期：6
• 页码：1661-1668
• 全文大小：354 K

文摘

The solvability of initial value problems for nonlinear Langevin equation involving two fractional orders are discussed in this paper. An existence result for the solution is obtained using the Leray-Schauder nonlinear alternative. In addition, sufficient conditions for unique solution are established under the Banach contraction principle. The existence results for the initial value problems of nonlinear classical Langevin equation follow as a special case of our results.