Open Journal of Mathematical Sciences (OMS)

In this paper, we suggest and analyze two new algorithm of fourth and fifth order convergence. We rewrite nonlinear equation as an equivalent coupled system and then use modified decomposition technique to develop our algorithms. Convergence analysis of newly introduced algorithms has been discussed. To see efficiency and performance of these algorithms, we have made comparison of these algorithms with some well known algorithms existing in literature.

In this work, we investigate the process of accretion for static spherical symmetric geometries for isotropic fluid. For analyze this process we use the nonminimal magnetically charged regular black holes. For this purpose, we obtain generalized expressions for the accretion rate \(\dot{M}\), critical radius \(r_s\), critical speed \(v^2_s\) and squared sound speed \(c^2_s\) during the accretion process near the regular black holes. Finally, we study the behavior of radial velocity, energy density and rate of change of mass for each
regular black hole by plotting graph.

The fractional calculus approach is used in the constitutive relationship model of fractional Maxwell fluid. Exact solutions for the velocity field and the adequate shear stress corresponding to the rotational flow of a fractional Maxwell fluid, between two infinite coaxial circular cylinders, are obtained by using the Laplace transform and finite Hankel transform for fractional calculus. The solutions that have been obtained are presented in terms of generalized \(G_{b, c, d}(\cdot, t)\) and \(R_{b, c}(\cdot, t)\) functions. In the limiting cases, the corresponding solutions for ordinary Maxwell and Newtonian fluids are obtained from our general solutions. Furthermore, the solutions for the motion between the cylinders, when one of them is at rest, are also obtained as special cases from our results. Finally, the influence of the material parameters on the fluid motion is underlined by graphical illustrations.