An efficient numerical approach for solving two-point fractional order nonlinear boundary value problems with Robin boundary conditions

Abstract This article proposes new strategies for solving two-point Fractional order Nonlinear Boundary Value Problems (FNBVPs) with Robin Conditions (RBCs). In the numerical schemes, a FNBVP is transformed into system of Initial (FIVPs) unknown (ICs). To approximate ICs in FIVPs, we develop nonlinear shooting methods based on Newton’s method and Halley’s using RBC at right end point. deal FIVPs system, mainly employ High-order Predictor–Corrector Methods (HPCMs) linear interpolation quadratic (Nguyen Jang Fract. Calc. Appl. Anal. 20(2):447–476, 2017) Volterra integral equations which are equivalent to FIVPs. The advantage proposed schemes HPCMs that even though they designed FNBVPs, can handle both (FBVPs) RBCs have uniform convergence rates HPCMs, $\mathcal{O}(h^{2})$ O ( h 2 ) $\mathcal{O}(h^{3})$ 3 techniques method, respectively. A variety examples demonstrated confirm effectiveness performance schemes. Also compare accuracy our another method.