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    Öğe
    Numerical solution of time-fractional coupled Korteweg-de Vries and Klein-Gordon equations by local meshless method
    (Indian Acad Sciences, 2021) Khan, Muhammad Nawaz; Ahmad, Imtiaz; Akgul, Ali; Ahmad, Hijaz; Thounthong, Phatiphat
    This article provides numerical simulations of the time-fractional coupled Korteweg-de Vries and Klein-Gordon equations via the local meshless collocation method (LMCM) utilising the radial basis functions. The recommended local meshless technique is utilised for the space derivatives of the models whereas Caputo fractional definition is used for time-fractional derivative. Numerical experiments are performed for one-dimensional coupled Korteweg-de Vries and two-dimensional Klein-Gordon equations. In order to verify the efficiency and accuracy of the proposed meshless method, numerical results are compared with exact and numerical techniques reported in recent literature which reveals that the method is computationally attractive and produces better results.
  • [ X ]
    Öğe
    On solutions of fuzzy fractional order complex population dynamical model
    (Wiley, 2023) Ullah, Abd; Ullah, Aman; Ahmad, Shabir; Ahmad, Imtiaz; Akgul, Ali
    Uncertainty always involved in our life activities because we cannot measure a physical quantity accurately. This situation has handled by fuzzy systems and fuzzy differential equations. Recently, fuzzy fractional differential equations got tremendous attention of the researchers of the current century because these operators model the real phenomenon more accurately than integer-order and fractional-order operators. Therefore, we investigate the complex population dynamical model under the fuzzy Caputo fractional derivative. Since the Laplace transform has a high convergence rate among all transform methods, so we use fuzzy Laplace transform along with Adomian decomposition to obtain general numerical results for the proposed model. We provide two examples to support the proposed procedure. We simulate the numerical results in terms of graphs for the various fractional-order and at uncertainty r is an element of [0, 1].