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Mixed monotone iterative technique for Hilfer fractional evolution equations with nonlocal conditions
Haide Gou,Yongxiang Li
Keywords:Mixed monotone iterative technique; coupled L-quasi-upper and lower solutions; Hilfer fractional derivative; noncompact measure
Abstract:
      The purpose of this paper is concerned with the existence of mild L-quasi-solutions for Hilfer fractional evolution equations with nonlocal conditions in an ordered Banach spaces E. By employing mixed monotone iterative technique, measure of noncompactness and Sadovskii’s fixed point theorem, we obtain the existence of mild L-quasi-solutions for Hilfer fractional evolution equations with noncompact semigroups. Finally, two examples are provide to illustrate the feasibility of our main results.