Browsing by Author "Atangana A."
Now showing 1 - 6 of 6
Results Per Page
Sort Options
Item The use of fractional order derivative to predict the groundwater flow(2013) Atangana A.; Bildik N.The aim of this work was to convert the Thiem and the Theis groundwater flow equation to the time-fractional groundwater flow model. We first derived the analytical solution of the Theim time-fractional groundwater flow equation in terms of the generalized Wright function. We presented some properties of the Laplace-Carson transform. We derived the analytical solution of the Theis-time-fractional groundwater flow equation (TFGFE) via the Laplace-Carson transform method. We introduced the generalized exponential integral, as solution of the TFGFE. This solution is in perfect agreement with the data observed from the pumping test performed by the Institute for Groundwater Study on one of its borehole settled on the test site of the University of the Free State. The test consisted of the pumping of the borehole at the constant discharge rate Q and monitoring the piezometric head for 350 minutes. © 2013 Abdon Atangana and Necdet Bildik.Item Existence and numerical solution of the Volterra fractional integral equations of the second kind(2013) Atangana A.; Bildik N.This work presents the possible generalization of the Volterra integral equation second kind to the concept of fractional integral. Using the Picard method, we present the existence and the uniqueness of the solution of the generalized integral equation. The numerical solution is obtained via the Simpson 3/8 rule method. The convergence of this scheme is presented together with numerical results. © 2013 Abdon Atangana and Necdet Bildik.Item Approximate solution of tuberculosis disease population dynamics model(2013) Atangana A.; Bildik N.We examine possible approximate solutions of both integer and noninteger systems of nonlinear differential equations describing tuberculosis disease population dynamics. The approximate solutions are obtained via the relatively new analytical technique, the homotopy decomposition method (HDM). The technique is described and illustrated with numerical example. The numerical simulations show that the approximate solutions are continuous functions of the noninteger-order derivative. The technique used for solving these problems is friendly, very easy, and less time consuming. © 2013 Abdon Atangana and Necdet Bildik.Item A generalized version of a low velocity impact between a rigid sphere and a transversely isotropic strain-hardening plate supported by a rigid substrate using the concept of noninteger derivatives(2013) Atangana A.; Ahmed O.A.; Bildik N.A low velocity impact between a rigid sphere and transversely isotropic strain-hardening plate supported by a rigid substrate is generalized to the concept of noninteger derivatives order. A brief history of fractional derivatives order is presented. The fractional derivatives order adopted is in Caputo sense. The new equation is solved via the analytical technique, the Homotopy decomposition method (HDM). The technique is described and the numerical simulations are presented. Since it is very important to accurately predict the contact force and its time history, the three stages of the indentation process, including (1) the elastic indentation, (2) the plastic indentation, and (3) the elastic unloading stages, are investigated. © 2013 Abdon Atangana et al.Item New iteration methods for time-fractional modified nonlinear kawahara equation(2014) Atangana A.; Bildik N.; Noutchie S.C.O.We put side by side the methodology of two comparatively new analytical techniques to get to the bottom of the system of nonlinear fractional modified Kawahara equation. The technique is described and exemplified with a numerical example. The dependability of both methods and the lessening in computations give these methods a wider applicability. In addition, the computations implicated are very simple and undemanding. © 2014 Abdon Atangana et al.Item Fractional calculus and its applications in applied mathematics and other sciences(Hindawi Publishing Corporation, 2014) Ray S.S.; Atangana A.; Noutchie S.C.O.; Kurulay M.; Bildik N.; Kilicman A.[No abstract available]