SEQUENTIAL FRACTIONAL DIFFERENTIAL EQUATIONS WITH PARAMETRIC TYPE ANTI-PERIODIC BOUNDARY CONDITIONS

We discuss the existence and uniqueness of solutions for sequential fractional differential equations supplemented with parametric type anti-periodic boundary conditions. We make use of fixed point theorems due to $ {\rm{Krasnosel'ski\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over i}}}$ and Banach to obtain the desired results. Examples illustrating the obtained results are presented. Moreover, an interesting feature concerning the solutions of parametric type anti-periodic boundary value problems of lower and higher order sequential fractional differential equations is presented (see the conclusions section). Our results are novel in the given configuration and generalize the literature on anti-periodic boundary value problems.