Abstract
The boundary value problems (BVPs) have attracted the attention of many scientists from both practical and theoretical points of view, for these problems have remarkable applications in different branches of pure and applied sciences. Due to this important property, this research aims to develop an efficient numerical method for solving a class of nonlinear fractional BVPs. The proposed method is free from perturbation, discretization, linearization, or restrictive assumptions, and provides the exact solution in the form of a uniformly convergent series. Moreover, the exact solution is determined by solving only a sequence of linear BVPs of fractional-order. Hence, from practical viewpoint, the suggested technique is efficient and easy to implement. To achieve an approximate solution with enough accuracy, we provide an iterative algorithm that is also computationally efficient. Finally, four illustrative examples are given verifying the superiority of the new technique compared to the other existing results.
Highlights
The application of boundary value problems (BVPs) can be found in different fields of pure and applied sciences; for instance, the narrow converting layers bounded by stable layers, which are believed to surround A-type stars, may be modeled by BVPs [1]
More discussions on the application of BVPs have been provided in Chandrasekhar [3], Baldwin [4], and Khalid et al [5]
The approximation schemes to solve non-linear BVPs can be found in different sources of numerical analysis [6, 7]
Summary
The application of boundary value problems (BVPs) can be found in different fields of pure and applied sciences; for instance, the narrow converting layers bounded by stable layers, which are believed to surround A-type stars, may be modeled by BVPs [1]. An existence theorem was discussed in Zhang and Su [34] for a linear fractional differential equation (FDE) with non-linear boundary conditions by using the method of upper and lower solutions in reverse order. In Arqub et al [35], a new kind of analytical method was proposed to predict and represent the multiplicity of solutions to non-linear fractional BVPs. In Khalil et al [36], the authors studied a coupled system of non-linear FDEs whose approximate solution was achieved under two different types of boundary conditions. In Asaduzzaman and Ali [38], the existence of positive solution was investigated to the BVPs for coupled system of non-linear FDEs. Motivated by the aforementioned statement, this manuscript aims to design a new iterative method to generate the approximate solution of non-linear fractional BVPs in the form of uniformly convergent series.
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