Browsing by Author "Ibrahim Mahariq"

Now showing 1 - 2 of 2
  • Default Image
    Item
    Study of implicit-impulsive differential equations involving Caputo-Fabrizio fractional derivative
    (American Institute of Mathematical Sciences, 2022) Thanin Sitthiwirattham; Rozi Gul; Kamal Shah; Ibrahim Mahariq; Jarunee Soontharanon; Khursheed J. Ansari; K. Shah; Department of Mathematics, University of Malakand, Chakdara Dir (Lower), Khyber Pakhtunkhawa, Pakistan; email: kamalshah408@gmail.com
    This article is devoted to investigate a class of non-local initial value problem of implicit-impulsive fractional differential equations (IFDEs) with the participation of the Caputo-Fabrizio fractional derivative (CFFD). By means of KrasnoselskiiÕs fixed-point theorem and BanachÕs contraction principle, the results of existence and uniqueness are obtained. Furthermore, we establish some results of Hyers-Ulam (H-U) and generalized Hyers-Ulam (g-H-U) stability. Finally, an example is provided to demonstrate our results. © 2022 the Author(s),.
  • Default Image
    Item
    Two-dimensional Haar Wavelet Method for Numerical Solution of Delay Partial Differential Equations
    (Hindawi Limited, 2022) Rohul Amin; Nichaphat Patanarapeelert; Muhammad Awais Barkat; Ibrahim Mahariq; Thanin Sitthiwirattham; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, Thailand; email: thanin-sit@dusit.ac.th
    In this paper, a two-dimensional Haar wavelet collocation method is applied to obtain the numerical solution of delay and neutral delay partial differential equations. Both linear and nonlinear problems can be solved using this method. Some benchmark test problems are given to verify the efficiency and accuracy of the aforesaid method. The results are compared with the exact solution and performance of the two-dimensional Haar collocation technique is measured by calculating the maximum absolute and root mean square errors for different numbers of grid points. The results are also compared with finite difference technique and one-dimensional Haar wavelet technique. The numerical results show that the two-dimensional Haar method is simply applicable, accurate and efficient. © 2022 Rohul Amin et al.