advection-diffusion equation and its related analytical solutions have gained wide applications in different areas. compared with numerical solutions, the analytical solutions benefit from some advantages. as such, many analytical solutions have been presented for the advection-diffusion equation. the difference between these solutions is mainly in the type of boundary conditions, e.g. time pat...

This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.

‎In this paper‎, ‎by using four functionals fixed point theorem‎, ‎we obtain sufficient conditions for the existence of‎ ‎at least one positive solution of an $n$th-order $m$-point boundary value problem‎. ‎As an application‎, ‎we give an example to demonstrate our main result.

‎in this paper‎, ‎by using four functionals fixed point theorem‎, ‎we obtain sufficient conditions for the existence of‎ ‎at least one positive solution of an $n$th-order $m$-point boundary value problem‎. ‎as an application‎, ‎we give an example to demonstrate our main result.

A new fixed point theorem on cones is applied to obtain the existence of at least two positive solutions of a higher-order three-point boundary value problem for the differential equation subject to a class of boundary value conditions. The associated Green's function is given. Some results obtained recently are generalized. 1. Introduction. The multipoint boundary value problems for ordinary d...

This paper presents an analytical solution for response of a piezoelectric hollow cylinder under two-dimensional electro thermo mechanical fields. The solution is based on a direct method and the Navier equations were solved using the complex Fourier series. The advantage of this method is its generality and from mathematical point of view, any type of the thermo mechanical and electrical bound...