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ON THE EXISTENCE RESULTS FOR A GENERALIZED P-LAPLACIAN FRACTIONAL BOUNDARY VALUE PROBLEM WITH INTEGRAL CONDITIONS
  • Rochdi Jebari
Rochdi Jebari
Shaqra University

Corresponding Author:[email protected]

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Abstract

The main purpose of this paper is to establish existence and multiplicity of positive solutions for a generalized p-Laplacian fractional differential equation with integral conditions: 8>>>>< >>>>: D 0+(ϕ(D 0+u(t))) + f(t; u(t)) = 0; t 2 [0; 1] u(0) = 0; u(1) = ∫ 1 0 u(s) dA(s): (ϕ(D 0+u(0)) = 0; (ϕ(D 0+u(1)) ′ = ∫ 1 0 ϕ(D 0+u(s)) dB(s): (0.1) where 1 < 2, 1 < 2, D 0+ and D 0+ are the standard Riemann-Liouville fractional derivatives, > 0 is a parameter. We derived explicit intervals of in which the uniqueness and multiplicity of solutions of problem are ensured. To prove our results, we used the strongly monotone operator principle and Guo-Krasnosel’skii xed-point theorem on cones. Four examples presented to illustrate our main results.