although homotopy-based methods, namely homotopy analysis method andhomotopy perturbation method, have largely been used to solve functionalequations, there are still serious questions on the convergence issue of thesemethods. some authors have tried to prove convergence of these methods, butthe researchers in this article indicate that some of those discussions are faulty.here, after criticizi...

We propose a new method of series analysis in which the available series coefficients are fitted to an algebraic equation. Such a proposal restricts solutions to have algebraic singularities with rational critical exponents. The advantage of the method over the method of differential approximants is that in those cases where the two methods are exact, the algebraic approximant method usually (t...

Various types of Coronaviruses are enveloped RNA viruses from the Corona-viridae family and part of the Coronavirinae subfamily. This family of viruses affects neurological, gastrointestinal, hepatic, and respiratory systems. Recently, a new memb-er of this family, named Covid-19, is moving around the world. The expansion of Covid-19 carries many risks, and its control requires strict planning ...

in this paper, the reduced dierential transform method is investigated fora nonlinear partial dierential equation modeling nematic liquid crystals, itis called the hunter-saxton equation. the main advantage of this methodis that it can be applied directly to nonlinear dierential equations withoutrequiring linearization, discretization, or perturbation. it is a semi analytical-numerical metho...

In this paper, a computational intelligence method is used for the solution of fractional optimal control problems (FOCP)'s with equality and inequality constraints. According to the Ponteryagin minimum principle (PMP) for FOCP with fractional derivative in the Riemann- Liouville sense and by constructing a suitable error function, we define an unconstrained minimization problem. In the optimiz...

Although homotopy-based methods, namely homotopy analysis method andhomotopy perturbation method, have largely been used to solve functionalequations, there are still serious questions on the convergence issue of thesemethods. Some authors have tried to prove convergence of these methods, butthe researchers in this article indicate that some of those discussions are faulty.Here, after criticizi...