Global existence and attractivity for Riemann-Liouville fractional semilinear evolution equations involving weakly singular integral inequalities

Abstract

Abstract In this paper, we obtain several results on the global existence, uniqueness and attractivity for fractional evolution equations involving the Riemann-Liouville type by exploiting some results on weakly singular integral inequalities in Banach spaces. Some boundedness conditions of the nonlinear term are considered to obtain the main results that generalize and improve some well-known works.

Keywords

• Fractional evolution equation
• Riemann-Liouville fractional derivative
• Existence
• Attractivity
• Weakly singular integral inequality