This paper is concerned with the existence and uniqueness of solutions for a new class boundary value problems, consisting by Hilfer-Hadamard fractional differential equations, supplemented nonlocal integro-multipoint conditions. The unique solution obtained via Banach contraction mapping principle, while results are established applying Schaefer Krasnoselskii fixed point theorems as well Leray...

the present paper investigates the potential application of graphene sheets with attached nanoparticles as resonant sensors by introducing a nonlocal shear deformation plate model. to take into account an elastic connection between the nanoplate and the attached nanoparticle, the nanoparticle is considered as a mass-spring system. then, a combination of pseudo-spectral and integral quadrature m...

In this paper we establish some existence results for nonlocal multivalued boundary-value problems. Our approach is based on existence results for operator inclusions involving a suitable closed-valued multifunction; see [2, 3]. Some applications are given.

We prove the existence of a positive solution for nonlocal problems involving the fractional Laplacian and a critical growth power nonlinearity when the equation is set in a suitable contractible domain.

The nonlocal boundary value problem        d 2 u(t) dt 2 + Au(t) = f (t)(0 ≤ t ≤ 1), du(t) dt + Au(t) = g(t)(−1 ≤ t ≤ 0), u(−1) = αu (µ) + βu (λ) + ϕ, |α|, |β| ≤ 1, 0 < µ, λ ≤ 1 for differential equation in a Hilbert space H with the self-adjoint positive definite operator A is considered. The stability estimates for the solution of this problem are established. In applications, the stab...

this paper proposed analytical solutions for the buckling analysis of rectangular single-layered graphene sheets under in-plane loading on all edges simply is supported. the characteristic equations of the graphene sheets are derived and the analysis formula is based on the nonlocal mindlin plate. this theory is considering both the small length scale effects and transverse shear deformation ef...