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POSITIVE SOLUTIONS FOR FRACTIONAL BOUNDARY VALUE PROBLEMS UNDER A GENERALIZED FRACTIONAL OPERATOR
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  • MDI BEGUM Jeelani,
  • Abdulkafi M. Saeed,
  • Mohammed S Abdo,
  • Kamal Shah
MDI BEGUM Jeelani
Department of Mathematics, Imam Muhammed Ibn Saud Islamic University
Abdulkafi M. Saeed
Department of Mathematics, College of Science, Qassim University
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Mohammed S Abdo
Department of Mathematics, Hodeidah University
Kamal Shah
Department of Mathematics, University of Malakand

Abstract

The work reported here concerns with study a generalized nonlinear fractional boundary value problems 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 the 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 have an effective role in the analysis. Some examples are offered to justify the validity of theoretical findings.