On antiperiodic boundary value problem for a semilinear differential inclusion of a fractional order 2 < q < 3

On antiperiodic boundary value problem for a semilinear differential inclusion of fractional order q. The investigation control systems with nonlinear units forms complicated and very important part contemporary mathematical theory harmonic analysis, which has numerous applications attracts the attention number researchers around world. In turn, development inclusions is associated fact that they provide convenient natural tool describing various classes, discontinuous characteristics, are studied in branches optimal theory, physics, radio acoustics etc. One best approaches to study this kind problems provided by methods multivalued distinguished as powerful, effective useful. However, solving these within frameworks existing theories often difficult problem, since many them find sufficiently adequate description terms equations derivatives. originates from ideas Leibniz Euler, but only end XX century, interest topic increased significantly. 70s - 80s, direction was greatly developed works A.A. Kilbas, S.G. Samko, O.I. Marichev, I. Podlubny, K.S. Miller, B. Ross, R. Hilfer, F. Mainardi, H. M. Srivastava. Notice research will open up prospects new opportunities studying non-standard specialists encounter while physical chemical processes porous, rarefied fractal media. It known periodic one classical inclusions. At same time, recent years, along problems, great due their physics interpolation problems.
 paper, we an Caputo derivative q Banach spaces. We assume map obeying conditions Caratheodory type, boundedness on bounded sets, regularity condition expressed measures noncompactness. first section, present necessary information Mittag -- Leffler function, noncompactness, condensing maps. second construct Green's function given then, introduce into consideration resolving integral operator space continuous functions. solutions fixed points multioperator. Therefore, use generalization Sadovskii type theorem prove existence. Then, multioperator upper semicontinuous respect two-component measure noncompactness proof main show transforms closed ball itself. Thus, obtain obeys all point existence problem.