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Lakshmikantham, V. and Devi, J.V. (2008) Theory of Fractional Differential Equations in Banach Space. European Journal of Pure and Applied Mathematics, 1, 38-45.

has been cited by the following article:

• TITLE: Fractional Differential Equations with Initial Conditions at Inner Points in Banach Spaces

  AUTHORS: Xiaoping Xu, Guangxian Wu, Qixiang Dong

  KEYWORDS: Fractional Derivative, Differential Equation, Initial Value Problem, Measure of Non-Compactness

  JOURNAL NAME: Advances in Pure Mathematics, Vol.5 No.14, December 7, 2015

  ABSTRACT: This paper is concerned with nonlinear fractional differential equations with the Caputo fractional derivatives in Banach spaces. Local existence results are obtained for initial value problems with initial conditions at inner points for the cases that the nonlinear parts are Lipschitz and non-Lipschitz, respectively. Hausdorff measure of non-compactness and Darbo-Sadovskii fixed point theorem are employed to deal with the non-Lipschitz case. The results obtained in this paper extend the classical Peano’s existence theorem for first order differential equations partly to fractional cases.