An optimal homotopy asymptotic method for finding solutions of non-linear fractional mathematical models / Okundalaye Oluwaseun Olumide

Okundalaye Oluwaseun , Olumide (2022) An optimal homotopy asymptotic method for finding solutions of non-linear fractional mathematical models / Okundalaye Oluwaseun Olumide. PhD thesis, Universiti Malaya.

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Abstract

This research project investigates the optimal solution procedure by constructing a fractional mathematical model with a conformable fractional derivative operator sense. Many real-life problems can be modelled more stably with fractional calculus due to its unique long memory feature and non-locality. An approximate analytical method (AAM) for an approximate analytical solution (AAS) has been employed in providing the solution to the model. One of the primary importance of using an AAS is to provide a solution where the exact solution is not available and had been established as one of the best solutions to address this model by many authors. However, the published studies have failed to establish the convergent criteria that guarantee accurate optimal values for the optimal solution. We addressed this challenge using the new optimal homotopy asymptotic method (OHAM) for optimal values for the accurate optimal solution. In this research, four fractional mathematical models with conformable fractional derivative operator sense have been modernized. We considered a fractional mathematical model of the steepest descent direction for equality non-linear constrained optimization problems in the first model. We considered a fractional mathematical model of the steepest descent direction for equality and inequality non-linear constrained optimization problems in the second model. In the third model, a fractional mathematical model for non-linear constrained optimal control problems is developed. In contrast, in the fourth model, we apply the proposed solution method for the non-linear fractional-order epidemic model (FOEM) of childhood disease prediction. The objective is to find the optimal solution, behaviour, and performance of the proposed fractional mathematical model (FMM) in the models. We produced a mathematical formulation and analysis of the problems inside the framework of the modification. A system of non-linear fractional differential equations with given initial conditions was provided for the proposed problems. Finally, we examined the results and compared them to previous works. Our results show a significant performance in fast convergence, actual optimal results, and provides more information about the complexity of the dynamics of the proposed models.

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