Abstract
A class of perturbed fractional nonlinear systems is studied. The dynamical system possesses two control parameters and a Lipschitz nonlinearity order of p-1. The multiplicity of the weak solutions is proved by means of the variational method and by Ricceri critical points theorems. An illustrative example is analyzed in order to highlight the obtained result.
Highlights
Fractional differential equations have proved to be promising tools in the modeling of diverse phenomena in various fields, such as physics, chemistry, biology, engineering and economics
There was a significant development in fractional differential equations due to the possibility of accounting for a larger class of memory properties
Critical point theory was very useful in determining the existence of solutions to complete differential equations with certain boundary conditions; see, for example, in the extensive literature on the subject, the classical books [17,18,19], and the references therein
Summary
Fractional differential equations have proved to be promising tools in the modeling of diverse phenomena in various fields, such as physics, chemistry, biology, engineering and economics. According to some assumptions, in [24], by using variational methods the authors obtained the existence of at least one weak solution for the following p-Laplacian fractional differential equation [24]:. Where αi ∈ (0; 1], φp(t) = |t|p–2t, t = 0, φp(0) = 0, p > 1,0 Dαt i and tDαTi are the left and right Riemann–Liouville fractional derivatives of order αi, respectively, for 1 ≤ i ≤ n, λ and μ are positive parameters, and F, G : [0, T] × Rn → R are measurable functions with respect to t ∈ [0, T] for every The left and right Riemann– Liouville fractional derivatives of order α > 0 for a function u are defined by aDαt u(t). It is desirable to give a verifiable consequence of Theorem 2 for a fixed text function ω
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