On the Λ-fractional spherical ballons

Deformations of spherical balloons under internal pressure in the micro or nano regions are discussed. Since the various conservation laws in those regions are not local, but globally valid, Λ-fractional analysis is considered. Globally minimizing the total energy function, the coexistence of phases phenomenon in Λ-fractional deformations is shown up. At the critical internal pressure, two equilibrium configurations of the balloon are revealed. The present analysis may be important in studying problems in biomembranes and not only.