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Volume 10, Number 5, 2020, Pages 1823-1847                                                                DOI:10.11948/20190211
Mixed monotone iterative technique for Hilfer fractional evolution equations with nonlocal conditions
Haide Gou,Yongxiang Li,Qixiang Li
Keywords:Mixed monotone iterative technique, coupled $L$-quasi-upper and lower solutions, Hilfer fractional derivative, measure of noncompactness.
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, an example is provide to illustrate the feasibility of our main results.
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