Solvability of Gripenberg's equations of fractional order with perturbation term in weighted LpL_p-spaces on R+{\mathbb{R}}^+

Abstract

This article deals with the solvability of Gripenberg's equations of fractional order with a perturbation term in weighted Lebesgue spaces on ${\mathbb{R}}^+=[0,\infty)$ via the fixed point hypothesis and the measure of noncompactness. The uniqueness of the solutions for the studied problem is discussed. An example is included to validate our results. The results presented in the article extend and generalize some former results in the available literature.