Abstract
In this paper, we study the existence of solutions for a boundary value problem of differential inclusions of order q ∈ (1,2] with non-separated boundary conditions involving convex and non-convex multivalued maps. Our results are based on the nonlinear alternative of Leray Schauder type and some suitable theorems of fixed point theory.
Highlights
Fractional calculus has proved to be an important tool in the modelling of dynamical systems associated with phenomena such as fractals and chaos
Differential inclusions arise in the mathematical modelling of certain problems in economics, optimal control, etc. and are widely studied by many authors; see [12,13,14,15] and the references therein
For some recent development on differential inclusions of fractional order, we refer the reader to the references [16,17,18,19,20,21]
Summary
Fractional calculus (differentiation and integration of arbitrary order) has proved to be an important tool in the modelling of dynamical systems associated with phenomena such as fractals and chaos. This branch of calculus has found its applications in various disciplines of science and engineering such as mechanics, electricity, chemistry, biology, economics, control theory, signal and image processing, polymer rheology, regular variation in thermodynamics, biophysics, blood flow phenomena, aerodynamics, electro-dynamics of complex medium, viscoelasticity and damping, control theory, wave propagation, percolation, identification, fitting of experimental data, etc. Where cDq denotes the Caputo fractional derivative of order q, F : [0, T ] × R → P(R) is a multivalued map, P(R) is the family of all subsets of R, and λ1, λ2, μ1, μ2 ∈ R
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