Geodesic
Positive solutions of boundary value problems for fractional differential equations involving the generalized proportional derivatives
Mohamed I. Abbas1 ; Mohamed I. Abbas
1Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria 21511, Egypt
Acta mathematica Universitatis Comenianae, Tome 91 (2022) no. 1, pp. 39-51 
Mohamed I. Abbas; Mohamed I. Abbas. Positive solutions of boundary value problems for fractional differential equations involving the generalized proportional derivatives. Acta mathematica Universitatis Comenianae, Tome 91 (2022) no. 1, pp. 39-51. http://geodesic.mathdoc.fr/item/AMUC_2022_91_1_a3/
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     author = {Mohamed I. Abbas and Mohamed I. Abbas},
     title = { Positive solutions of boundary value problems for fractional differential equations involving the generalized proportional derivatives},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {39--51},
     year = {2022},
     volume = {91},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2022_91_1_a3/}
}
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This paper is concerned with the existence and uniqueness of positive solutions of boundary value problems for fractional differential equations involving the generalized proportional derivatives of Caputo type. The investigation of the proposed BVP depends on the properties of the Green function, the method of upper and lower solutions, and the fixed point theorems due to Schauder and Banach. An example is proposed to clarify the applicability of the theoretical results.