Nasser Al-Salti

On a Differential Equation with Caputo-Fabrizio Fractional Derivative of Order 1 <β ≤ 2 and Application to Mass-Spring-Damper System

In this work, we investigate a linear differential equation involving Caputo-Fabrizio fractional derivative of order

Buoyancy Induced Heat Transfer Flow Inside a Tilted Square Enclosure Filled with Nanofluids in the Presence of Oriented Magnetic Field

1<\beta\leq 2

Initial boundary value problems for a fractional differential equation with hyper-Bessel operator

. Under some assumptions the considered equation is reduced to an integer order differential equation and solutions for different cases are obtained in explicit forms. We also prove a uniqueness of a solution of an initial value problem with a nonlinear differential equation containing the Caputo-Fabrizio derivative. Application of our result to the mass-spring-damper motion is also presented.

Inverse source problem for multi-term fractional mixed type equation

ABSTRACT This paper analyzes heat transfer and fluid flow of natural convection in an inclined square enclosure filled with different types of nanofluids having various shapes of nanoparticles in the presence of oriented magnetic field. The Galerkin weighted residual finite element method has been employed to solve the governing non-dimensional partial differential equations. In the numerical simulations, water, ethylene glycol, and engine oil containing copper, alumina, titanium dioxide nanoparticles are considered. The effects of model parameters such as Rayleigh number, Hartmann number, nanoparticles volume fraction, magnetic field inclination angle, geometry inclination angle on the fluid flow and heat transfer are investigated. The results indicate that increment of the Rayleigh number and nanoparticle volume fraction increase the heat transfer rate in a significant way, whereas, increment of the Hartmann number decreases the overall heat transfer rate. It is also observed that a blade shape nanoparticle gives higher heat transfer rate compared to other shapes of nanoparticles. The critical geometry inclination angle at which the maximum heat transfer rate is achieved depends on the nanoparticle volume fraction as well as on the magnetic field orientation. These results are new and have direct applications in solar thermal collectors and thermal insulator of buildings.

Hydromagnetic slip flow of water based nanofluids past a wedge with convective surface in the presence of heat generation (or) absorption

Abstract Direct and inverse source problems of a fractional diffusion equation with regularized Caputo-like counterpart of a hyper-Bessel differential operator are considered. Solutions to these problems are constructed based on appropriate eigenfunction expansions and results on existence and uniqueness are established. To solve the resultant equations, a solution to such kind of non-homogeneous fractional differential equation is also presented.

Hydromagnetic natural convective heat transfer flow in an isosceles triangular cavity filled with nanofluid using two-component nonhomogeneous model

In this work, we investigate an inverse source problem for multi-term fractional mixed type equation in a rectangular domain. We seek solutions in a form of series expansions using orthogonal basis obtained by using the method of a separation of variables. The obtained solutions involve multi-variable Mittag-Leffler functions, and hence, certain properties of the multi-variable Mittag-Leffler function needed for our calculations were established and proved. Imposing certain conditions to the given data, the convergence of the infinite series solutions was proved as well.