Abstract
We study the existence of solutions for a class of fractional differential inclusions with anti-periodic boundary conditions. The main result of the paper is based on Bohnenblust- Karlins fixed point theorem. Some applications of the main result are also discussed.
Highlights
In some cases and real world problems, fractional-order models are found to be more adequate than integer-order models as fractional derivatives provide an excellent tool for the description of memory and hereditary properties of various materials and processes
Antiperiodic boundary value problems have recently received considerable attention as antiperiodic boundary conditions appear in numerous situations, for instance, see 15–22
Differential inclusions arise in the mathematical modelling of certain problems in economics, optimal control, and so forth. and are widely studied by many authors, see 23– 27 and the references therein
Summary
In some cases and real world problems, fractional-order models are found to be more adequate than integer-order models as fractional derivatives provide an excellent tool for the description of memory and hereditary properties of various materials and processes. The mathematical modelling of systems and processes in the fields of physics, chemistry, aerodynamics, electro dynamics of complex medium, polymer rheology, and so forth, involves derivatives of fractional order. Differential inclusions arise in the mathematical modelling of certain problems in economics, optimal control, and so forth. Chang and Nieto 33 discussed the existence of solutions for the fractional boundary value problem:. We consider the following fractional differential inclusions with antiperiodic boundary conditions cDqx t ∈ F t, x t , t ∈ 0, T , T > 0, 1 < q ≤ 2, 1.2 x 0 −x T , x 0 −x T , where cDq denotes the Caputo fractional derivative of order q, F : 0, T × R → 2R \ {∅}. Bohnenblust-Karlin fixed point theorem is applied to prove the existence of solutions of 1.2
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