Comparison principles for differential equations involving Caputo fractional derivative with Mittag-Leffler non-singular kernel
 作者： Mohammed Al-Refai 作者单位： 1UAE University, Al Ain, UAE 刊名： Electronic Journal of Differential Equations, 2018, Vol.2018 (36,), pp.1-10 来源数据库： Directory of Open Access Journals 关键词： Fractional differential equations;  Maximum principle; 原始语种摘要： In this article we study linear and nonlinear differentialequations involving the Caputo fractional derivative with Mittag-Lefflernon-singular kernel of order $0<\alpha<1$.We first obtain a new estimate of the fractional derivative of a functionat its extreme points and derive a necessary condition for the existenceof a solution to the linear fractional equation. The condition obtaineddetermines the initial condition of the associated fractionalinitial-value problem. Then we derive comparison principles for thelinear fractional equations, and apply these principles for obtaining normestimates of solutions and to obtain a uniqueness results.We also derive lower and upper bounds of solutions. The applicability ofthe new results is illustrated through several examples.

• fractional　分级的
• kernel
• singular　奇异的
• derivative　衍生物
• derive　导出
• differential　差动的
• applicability　适用性
• uniqueness　唯一性
• illustrated　以…说明
• apply　应用