Advances in Analysis

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DOI: 10.22606/aan.2017.11001

• Mengna Zhang^*
  School of Mechanical Engineering, Shandong University, Jinan, 250061, P. R. China
• Yansheng Liu^*
  Department of Mathematics, Shandong Normal University, Jinan, 250014, P. R. China

This article concerns the existence of solutions for implicit fractional differential systems with coupled nonlocal conditions of functional type. We use a vectorial version of Krasnoselskii’s fixed point theorem in generalized metric space to overcome the lack of complete continuity of the associated integral operators. Moreover, the sufficient conditions for the existence will be weakened on the subinterval in which our nonlocal conditions act. An example is presented to illustrate the theory.

Fractional differential systems, implicit differential equation, coupled nonlocal conditions, fixed point, vector-valued norm, spectral radius of a matrix.

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