Well-posedness of a class of singular Volterra integral equations on the L^p (p ≥1) space

Abstract:

Motivated by fractional differential equations, we consider the well-posedness of a class of singular Volterra integral equations on the L^p (p ≥1) space by using the fixed point theorem, generalize and improve the known results. Particularly, the well-posedness of Riemann--Liouville fractional order ordinary differential equations can be regarded as a special case of our results.

Key words:Singular Volterra integral equation; Well-posedness; Fractional differential equation; L^p (p ≥1) space