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Browsing by Author "Shaikh, Amjad"

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    Citation Count: Shaikh, Amjad...et al. (2019). Analysis of differential equations involving Caputo-Fabrizio fractional operator and its applications to reaction-diffusion equations", Advances in Difference Equations.
    Analysis of differential equations involving Caputo-Fabrizio fractional operator and its applications to reaction-diffusion equations
    (Springer Open, 2019) Shaikh, Amjad; Tassaddiq, Asifa; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; 56389
    This manuscript deals with fractional differential equations including Caputo-Fabrizio differential operator. The conditions for existence and uniqueness of solutions of fractional initial value problems is established using fixed point theorem and contraction principle, respectively. As an application, the iterative Laplace transform method (ILTM) is used to get an approximate solutions for nonlinear fractional reaction-diffusion equations, namely the Fitzhugh-Nagumo equation and the Fisher equation in the Caputo-Fabrizio sense. The obtained approximate solutions are compared with other available solutions from existing methods by using graphical representations and numerical computations. The results reveal that the proposed method is most suitable in terms of computational cost efficiency, and accuracy which can be applied to find solutions of nonlinear fractional reaction-diffusion equations.