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 equationsMaximum 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.
全文获取路径: DOAJ  (合作)

  • 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