Some analytical and numerical results for a fractional q-differential inclusion problem with double integral boundary conditions

In this work, we study a q-differential inclusion with doubled integral boundary conditions under the Caputo derivative. To achieve the desired result, we use the endpoint property introduced by Amini-Harandi and quantum calculus. Integral boundary conditions were considered on time scale $\mathcal{T}_{t_{0}}=\{t_{0},t_{0}q,t_{0}q^{2}, \ldots\}\cup \{0\}$ T t 0 = { t 0 , t 0 q , t 0 q 2 , … } ∪ { 0 } . To better evaluate the validity of our results, we provided an example, some graphs, and tables.

Periodic solutions for a differential inclusion problem involving the p(t)-Laplacian

In the present paper, we consider the nonlinear periodic systems involving variable exponent driven by p(t)-Laplacian with a locally Lipschitz nonlinearity. Our arguments combine the variational principle for locally Lipschitz functions with the properties of the generalized Lebesgue-Sobolev space. Applying the non-smooth critical point theory, we establish some new existence results.

Piecewise affine stress-free martensitic inclusions in planar nonlinear elasticity

We consider a partial differential inclusion problem which models stress-free martensitic inclusions in an austenitic matrix, based on the standard geometrically nonlinear elasticity theory. We show that for specific parameter choices there exist piecewise affine continuous solutions for the square-to-oblique and the hexagonal-to-oblique phase transitions. This suggests that for specific crystallographic parameters the hysteresis of the phase transformation will be particularly small.