In this article, we survey the asymptotic stability analysis of fractional differential systems with the Prabhakar fractional derivatives. We present the stability regions for these types of fractional differential systems. A brief comparison with the stability aspects of fractional differential systems in the sense of Riemann-Liouville fractional derivatives is also given. 

Viscoelastic fluids, such as polymers, paints, and DNA suspensions, are almost everywhere very useful in the industry. This article aims to study significance of ramped temperature dynamics viscoelastic fluid. Magnetohydrodynamic (MHD) effect is considered presence Lorentz force. The flow a porous medium using generalized Darcy’s law. Heat transfers through convection, fluid near plate takes he...

This paper systematically explains how to apply the invariant subspace method using variable transformation for finding exact solutions of (k+1)-dimensional nonlinear time-fractional PDEs in detail. More precisely, we have shown transform given into (1+1)-dimensional procedure. Also, explain derive reduced equations method. Additionally, this careful and systematic study, will investigate find ...

The structure of Bénard–Marangoni convection cells can be controlled by periodic topographic patterns on the heated surface that generates the convection. When the periodicity of the topographic pattern matches the intrinsic periodicity of the convection cells, a convective pattern is formed that is 1:1 commensurate with the topographic pattern. Arrays of hexagonal, square, and triangular conve...

[1] For the first time precise measurements obtained using Super Dual Auroral Radar Network (SuperDARN) radars are used to quantify the temporal variability in the convection velocity and identify the cause of the variations for a particular event located in the vicinity of the cusp. Using SuperDARN line-of-sight (LOS) Doppler velocities near 1200 magnetic local time and a standard fitting tech...

We report the numerical simulations of the horizontal convection within a rectangle cavity tank at high Rayleigh numbers. The physical solution of horizontal convection depends on the spatial resolution of the meshes. The necessary mesh number N is proportion to Ra. The unstable numerical solutions are obtained asN < cRa. This power law also implies that the spatial resolution is dominated by v...

  The effect of magnetic field on an incompressible (Kuvshiniski-Type) viscoelastic rotating fluid heated from below in porous medium is considered. For the case of stationary convection, magnetic field and medium permeability have both stabilizing and destabilizing effect on the thermal convection under some conditions whereas rotation has a stabilizing effect on the thermal convection. In the...

in this paper, under appropriate oscillating behaviours of the nonlinear term, we prove some multiplicity results for a class of nonlinear fractional equations. these problems have a variational structure and we find three solutions for them by exploiting an abstract result for smooth functionals defined on a reflexive banach space. to make the nonlinear methods work, some careful analysis of t...

in this paper we apply hybrid functions of general block-pulse‎ ‎functions and legendre polynomials for solving linear and‎ ‎nonlinear multi-order fractional differential equations (fdes)‎. ‎our approach is based on incorporating operational matrices of‎ ‎fdes with hybrid functions that reduces the fdes problems to‎ ‎the solution of algebraic systems‎. ‎error estimate that verifies a‎ ‎converge...

in this paper, a new numerical method for solving fractional optimal control problems (focps) is presented. the fractional derivative in the dynamic system is described in the caputo sense. the method is based upon biorthogonal cubic hermite spline multiwavelets approxima-tions. the properties of biorthogonal multiwavelets are first given. the operational matrix of fractional riemann-lioville i...