Differential equation with fractional order have recently proved valuable tools in the modeling of many phenomena in various fields of science and engineering [1-5]. Recently, many researchers paid attention to existence result of solution of the boundary value problems for fractional differential equations at nonresonance, see for examples [6-15]. But, there are few papers which consider the b...

although elzaki transform is stronger than sumudu and laplace transforms to solve the ordinary differential equations withnon-constant coefficients, but this method does not lead to finding the answer of some differential equations. in this paper, a method is introduced to find that a differential equation by elzaki transform can be ‎solved?‎

Nonlinear vibration of a fluid-filled single walled carbon nanotube (SWCNT) with simply supported ends is investigated in this paper based on Von-Karman’s geometric nonlinearity and the simplified Donnell’s shell theory. The effects of the small scales are considered by using the nonlocal theory and the Galerkin's procedure is used to discretize partial differential equations of the governing i...

in the present study an alternative model allows the extension of the debye-hückel theory (dht) considering time dependence explicitly. from the electro-quasistatic approach (eqs) done in earlier studies time dependent potentials are suitable to describe several phenomena especially conducting media as well as the behaviour of charged particles in arbitrary solutions acting as electrolytes.this...

Keywords: Frobenius integrable decompositions Partial differential equations Differential polynomials Bäcklund transformations Ordinary differential equations Nonlinearity a b s t r a c t Frobenius integrable decompositions are presented for a kind of ninth-order partial differential equations of specific polynomial type. Two classes of such partial differential equations possessing Frobenius i...

In this paper, we are interested in the phenomenon of blow up in finite time (or formation of singularity in finite time) of solutions of the critical generalized KdV equation. Few results are known in the context of partial differential equations with a Hamiltonian structure. For the semilinear wave equation, or more generally for hyperbolic systems, the finite speed of propagation allows one ...

Abstract: In this paper , for the nonlinear Cahn-Hilliard equation, we give its symmetry group by the approximate generalized conditional symmetry. As the application of approximate generalized conditional symmetry, the initial-value problem of the partial differential equations can be reduced to perturbed initial-value problem for a system of perturbed first-order ordinary differential equatio...

In this paper, an aproximate analytical method called the differential transform method (DTM) is used as a tool to give approximate solutions of nonlinear oscillators with fractional nonlinearites. The differential transformation method is described in a nuthsell. DTM can simply be applied to linear or nonlinear problems and reduces the required computational effort. The proposed scheme is base...

We consider the pair diffusion process which includes cluster reactions of high order. We are able to prove a local (in time) existence result in arbitrary space dimensions. The model includes a nonlinear system of reaction-drift-diffusion equations, a nonlinear system of ordinary differential equations in Banach spaces, and a nonlinear elliptic equation for the electrochemical potential. The l...