scholarly journals UPPER AND LOWER SOLUTION METHOD FOR FRACTIONAL EVOLUTION EQUATIONS WITH ORDER 1 < α < 2

2014 ◽  
Vol 51 (6) ◽  
pp. 1123-1139 ◽  
Author(s):  
Xiao-Bao Shu ◽  
Fei Xu
Keyword(s):  
Solution Method ◽  
Evolution Equations ◽  
Lower Solution ◽  
Fractional Evolution Equations ◽  
Upper And Lower Solution ◽  
Lower Solution Method

scholarly journals Upper and lower solution method for Hilfer fractional evolution equations with nonlocal conditions

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Haide Gou ◽  
Yongxiang Li
Keyword(s):  
Banach Space ◽  
Solution Method ◽  
Measure Of Noncompactness ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Lower Solution ◽  
Ordered Banach Space ◽  
Fractional Evolution Equations ◽  
Lower Solution Method

AbstractThis paper is concerned with the existence of extremal mild solutions for Hilfer fractional evolution equations with nonlocal conditions in an ordered Banach space E. By employing the method of lower and upper solutions, the measure of noncompactness, and Sadovskii’s fixed point theorem, we obtain the existence of extremal mild solutions for Hilfer fractional evolution equations with noncompact semigroups. Finally, an example is provided to illustrate the feasibility of our main results.

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