The main objective of this work is to present a modification the Mittag- Leffler function deduce relatively new analytical approximate method (for short MMLFM) able solve time-fractional nonlinear partial differential equations (PDEs). Moreover, we employ MMLFM coupled Korteweg-de Vries (KdV) model described by two fractional (FPDEs) based upon Caputo derivative (CFD). simulation projected resu...

All the equations of the KdV hierarchy share many common features, like single and multiple soliton solutions, singular algebraic potentials, etc.; in particular the phase shifts for solitonsoliton scattering are all the same in the chain KdV1, KdV2, etc., depending only on the momenta. We exhibit the reason for this behaviour: as these equations are originated as isopectral deformations of the...

We obtain the conserved, nonlocal charges for the supersymmetric two boson hierarchy from fractional powers of its Lax operator. We show that these charges reduce to the ones of the supersymmetric KdV system under appropriate reduction. We study the algebra of the nonlocal, local and supersymmetry charges with respect to the first and the second Hamiltonian structures of the system and discuss ...

R. Hirota and K. Kimura discovered integrable discretizations of the Euler and the Lagrange tops, given by birational maps. Their method is a specialization to the integrable context of a general discretization scheme introduced by W. Kahan and applicable to any vector field with a quadratic dependence on phase variables. According to a proposal by T. Ratiu, discretizations of the Hirota-Kimura...

Effects of the uniform transverse magnetic field on the transient free convective flows of a nanofluid with generalized thermal transport between two vertical parallel plates have been analyzed. The fluid temperature is described by a time-fractional differential equation with Caputo derivatives. Closed form of the temperature field is obtained by using the Laplace transform and fractional deri...

In this article, we study and investigate the analytical solutions of space-time nonlinear fractional modified KDV-Zakharov-Kuznetsov (mKDV-ZK) equation. We have got new exact mKDV-ZK equation by using first integral method; found types hyperbolic trigonometric symbolic computation.

The variational iteration method [1, 2], which is a modified general Lagrange multiplier method, has been shown to solve effectively, easily, and accurately a large class of nonlinear problems with approximations which converges (locally) to accurate solutions (if certain Lipschitz-continuity conditions are met). It was successfully applied to autonomous ordinary differential equations and nonl...

Considering the importance of ever-increasing interest in exploring localized waves, we investigate a generalized (3+1)-dimensional Hirota-Satsuma-Ito equation describing unidirectional propagation shallow-water waves and perform Painlev\'e analysis to understand its integrability nature. We construct explicit form higher-order rogue wave solutions by adopting Hirota's bilinearization polynomia...

in this article, we investigate sufficient conditions for existence of maximal and minimalsolutions to a coupled system of highly nonlinear differential equations of fractional order with mixedtype boundary conditions. to achieve this goal, we apply monotone iterative technique togetherwith the method of upper and lower solutions. also an error estimation is given to check theaccuracy of the me...