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Existence and nonexistence results for a system of integral boundary value problems with parametric dependence

Bourguiba Rim (University of Monastir, Faculty of Sciences of Monastir, LRES, Monastir, Tunisia), Rym.Bourguiba@fsm.rnu.tn
Toumi Faten (King Faisal University, College of Business Administration, Ahsaa, Saoudi Arabia), ftowmi@kfu.edu.sa
Wanassi Om Kalthoum (University of Monastir, Faculty of Sciences of Monastir, LRES, Monastir, Tunisia), omkalthoum.wannassi@fsm.rnu.tn

In this paper, we are concerned with a class of system of nonlinear singular fractional differential equations with integral boundary conditions. More precisely, we establish sufficient conditions for existence, multiplicity and nonexistence of positive solutions. The results are derived in terms of different values of the parameters. Our approach relies on the Krasnoselskii’s fixed point theorem. Some examples are given to illustrate our main results.

Keywords: Fractional differential system, positive solution, integral boundary conditions, Green’s functions, dependence on a parameter