Advances in Analysis

Download PDF (246.7 KB) PP. 9 - 16 Pub. Date: April 2, 2019

DOI: 10.22606/aan.2019.42001

• Shuqin Zhang^*
  Department of Mathematics, China University of Mining and Technology, Beijing, China
• Shanshan Li
  Department of Mathematics, China University of Mining and Technology, Beijing, China

Some experts claim that the Riemann-Liouville variable-order fractional integral didn’t have semigroup property. This property brought us extreme difficulties when we consider the unique existence of solutions of variable-order fractional differential equations. In this work, based on some analysis technique, by means of fixed point theorem, we consider the existence of solutions to an initial value problem for differential equations of variable-order involving with variable-order fractional integral.

Variable-order fractional derivative, initial value problem, fractional differential equations, solution, fixed point theorem

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