Browsing by Author "Tassaddiq, Asifa"

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Citation Count: Tassaddiq, Asifa...et al. (2021). "A New Three-Step Root-Finding Numerical Method and Its Fractal Global Behavior", Fractal and Fractional, Vol. 5, No. 4.
A New Three-Step Root-Finding Numerical Method and Its Fractal Global Behavior
(2021) Tassaddiq, Asifa; Qureshi, Sania; Soomro, Amanullah; Hincal, Evren; Baleanu, Dumitru; Shaikh, Asif Ali; 56389
There is an increasing demand for numerical methods to obtain accurate approximate solutions for nonlinear models based upon polynomials and transcendental equations under both single and multivariate variables. Keeping in mind the high demand within the scientific literature, we attempt to devise a new nonlinear three-step method with tenth-order convergence while using six functional evaluations (three functions and three first-order derivatives) per iteration. The method has an efficiency index of about 1.4678, which is higher than most optimal methods. Convergence analysis for single and systems of nonlinear equations is also carried out. The same is verified with the approximated computational order of convergence in the absence of an exact solution. To observe the global fractal behavior of the proposed method, different types of complex functions are considered under basins of attraction. When compared with various well-known methods, it is observed that the proposed method achieves prespecified tolerance in the minimum number of iterations while assuming different initial guesses. Nonlinear models include those employed in science and engineering, including chemical, electrical, biochemical, geometrical, and meteorological models.
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.