In this paper, we establish exact solutions for the time-fractional Klein-Gordon equation, and the time-fractional Hirota-Satsuma coupled KdV system. The He’s semi-inverse and the Kudryashov methods are used to construct exact solutions of these equations. We apply He’s semi-inverse method to establish a variational theory for the time-fractional Klein-Gordon equation, and the time-fractiona...

In the present study, nonlinear vibration of coupled carbon nanotubes (CNTs) in presence of surface effect is investigated based on nonlocal Euler-Bernoulli beam (EBB) theory. CNTs are embedded in a visco-elastic medium and placed in the uniform longitudinal magnetic field. Using von Kármán geometric nonlinearity and Hamilton’s principle, the nonlinear higher order governing equations are deriv...

a modified f-expansion method to find the exact traveling wave solutions of  two-component nonlinear partial differential equations (nlpdes) is discussed. we use this method to construct many new solutions to the nonlinear whitham-broer-kaup system (1+1)-dimensional. the solutions obtained include jacobi elliptic periodic wave solutions which exactly degenerate to the soliton solutions, triangu...

A modified F-expansion method to find the exact traveling wave solutions of  two-component nonlinear partial differential equations (NLPDEs) is discussed. We use this method to construct many new solutions to the nonlinear Whitham-Broer-Kaup system (1+1)-dimensional. The solutions obtained include Jacobi elliptic periodic wave solutions which exactly degenerate to the soliton solutions, triangu...

in the present research, nonlinear vibration in a coupled system of boron-nitride nano-tube reinforced composite (bnntrc) oil pipes is studied. single-walled boron-nitride nano-tubes (swbnnts) are arranged in a longitudinal direction inside poly-vinylidene fluoride (pvdf) matrix. damping and shearing effects of surrounded medium are taken into account by visco-pasternak model. based on piezoele...

we consider the coupled system$f(x,y)=g(x,y)=0$,where$$f(x, y)=bs 0 {m_1}   a_k(y)x^{m_1-k}mbox{ and } g(x, y)=bs 0 {m_2} b_k(y)x^{m_2-k}$$with entire functions $a_k(y), b_k(y)$.we    derive a priory estimates  for the sums of the rootsof the considered system andfor the counting function of  roots.

In this study, forced-vibration analysis of a coupled system of single layered graphene sheets (SLGSs) subjected to the moving nano-particle is carried out based on nonlocal elasticity theory of orthotropic plate. Two SLGSs are coupled with elastic medium which is simulated by Pasternak and Visco-Pasternak models. Using Hamilton’s principle, governing differential equations of motion are derive...

In the present research, nonlinear vibration in a coupled system of Boron-Nitride nano-tube reinforced composite (BNNTRC) oil pipes is studied. Single-walled Boron-Nitride nano-tubes (SWBNNTs) are arranged in a longitudinal direction inside Poly-vinylidene fluoride (PVDF) matrix. Damping and shearing effects of surrounded medium are taken into account by visco-Pasternak model. Based on piezoele...

As two-dimensional coupled system of nonlinear partial differential equations does not give enough smooth solutions, when approximated by linear, quadratic and cubic polynomials and gives poor convergence or no convergence. In such cases, approximation by zero degree polynomials like Haar wavelets (continuous functions with finite jumps) are most suitable and reliable. Therefore, modified numer...