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Positive solutions for fractional boundary value problems under a generalized fractional operator
Author(s) -
Jeelani Mdi B.,
Saeed Abdulkafi M.,
Abdo Mohammed S.,
Shah Kamal
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7377
Subject(s) - mathematics , uniqueness , fractional calculus , boundary value problem , operator (biology) , cone (formal languages) , mathematical analysis , fixed point theorem , nonlinear system , type (biology) , biochemistry , chemistry , physics , repressor , algorithm , quantum mechanics , transcription factor , gene , ecology , biology
The work reported here concerns the study of a generalized nonlinear fractional boundary value problem involving ϑ ‐fractional derivative in the Riemann–Liouville sense. The existence and uniqueness of positive solutions to the problem at hand are proved. Our discussion relies on the properties of Green's function, the upper and lower solutions method, and the classical fixed point theorems in a cone. Moreover, building upper and lower control functions has an effective role in the analysis. Some examples are given to justify the validity of theoretical results.