Asian Research Journal of Mathematics <p style="text-align: justify;"><strong>Asian Research Journal of Mathematics (ISSN: 2456-477X)</strong> aims to publish high-quality papers (<a href="/index.php/ARJOM/general-guideline-for-authors">Click here for Types of paper</a>) in all areas of ‘Mathematics and Computer Science’. By not excluding papers on the basis of novelty, this journal facilitates the research and wishes to publish papers as long as they are technically correct and scientifically motivated. The journal also encourages the submission of useful reports of negative results. This is a quality controlled, OPEN peer-reviewed, open access INTERNATIONAL journal.</p> SCIENCEDOMAIN international en-US Asian Research Journal of Mathematics 2456-477X LHAM Approach to Fractional Order Rosenau-Hyman and Burgers' Equations <p>Fractional calculus has been found to be a great asset in finding fractional dimension in chaos&nbsp;theory, in viscoelasticity diffusion, in random optimal search etc. Various techniques have been&nbsp;proposed to solve differential equations of fractional order. In this paper, the Laplace-Homotopy&nbsp;Analysis Method (LHAM) is applied to obtain approximate analytic solutions of the nonlinear&nbsp;Rosenau-Hyman Korteweg-de Vries (KdV), K(2, 2), and Burgers' equations of fractional order&nbsp;with initial conditions. The solutions of these equations are calculated in the form of convergent&nbsp;series. The solutions obtained converge to the exact solution when α = 1, showing the reliability&nbsp;of LHAM.</p> S. O. Ajibola A. S. Oke W. N. Mutuku ##submission.copyrightStatement## 2020-05-14 2020-05-14 1 14 10.9734/arjom/2020/v16i630192 Effects of Some Flow Parameters on Unsteady MHD Fluid Flow Past a Moving Vertical Plate Embedded in Porous Medium in the Presence of Hall Current and Rotating System <p>This paper is on the numerical study of the effects of some flow parameters like Hall current, rotation, thermal diffusion (Soret) and diffusion thermo (Dufour) on unsteady magnetohydrodynamic natural convective heat and mass transfer of a viscous, rotating, electrically conducting and incompressible fluid flow past an impulsively moving vertical plate embedded in porous medium. The fundamental governing dimensionless coupled boundary layer partial differential equations are solved by the method of lines (MOL). Computations are then performed to determine the effects of the governing flow parameters. The results show that an increase in Soret number, Dufour number and Hall current parameter, causes an increase in the primary and secondary velocities of the fluid flow. As rotating parameter increases, the primary velocity of the flow decreases. Similarly, as Dufour and Soret numbers increase, the temperature and concentration profiles of the fluid flow increase. The effects of the flow parameters on primary and secondary velocity, temperature and concentration fields for externally cooling of the plate are shown graphically.</p> M. O. Durojaye K. A. Jamiu F. O. Ogunfiditimi ##submission.copyrightStatement## 2020-05-15 2020-05-15 15 29 10.9734/arjom/2020/v16i630193 Optimal Bounds of the Arithmetic Mean by Harmonic, Contra-harmonic and New Seiffert-like Means <p>We provide the optimal bounds for the arithmetic mean in terms of harmonic, contra-harmonic and new Seiffert-like means.</p> Hui-Zuo Xu Wei-Mao Qian ##submission.copyrightStatement## 2020-05-19 2020-05-19 30 36 10.9734/arjom/2020/v16i630195 On Sums of Cubes of Generalized Fibonacci Numbers: Closed Formulas of Σn k=0 kW3 k and Σn k=1 kW3− k <p>In this paper, closed forms of the sum formulas Σn k=0 kW3 k and Σn k=1 kW3-k for the cubes of generalized Fibonacci numbers are presented. As special cases, we give sum formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas numbers. We present the proofs to indicate how these formulas, in general, were discovered. Of course, all the listed formulas may be proved by induction, but that method of proof gives no clue about their discovery. Our work generalize second order recurrence relations.</p> Yuksel Soykan ##submission.copyrightStatement## 2020-05-24 2020-05-24 37 52 10.9734/arjom/2020/v16i630196