Shiri, BabakBaleanu, Dumitru2024-04-252025-09-182024-04-252025-09-182022Baleanu, Dumitru; Shiri, Babak. (2022). "Nonlinear higher order fractional terminal value problems", AIMS Mathematics, Vol.7, No.5, pp.7489-7506.2473-6988https://doi.org/10.3934/math.2022420https://hdl.handle.net/20.500.12416/13892Terminal value problems for systems of fractional differential equations are studied with an especial focus on higher-order systems. Discretized piecewise polynomial collocation methods are used for approximating the exact solution. This leads to solving a system of nonlinear equations. For solving such a system an iterative method with a required tolerance is introduced and analyzed. The existence of a unique solution is guaranteed with the aid of the fixed point theorem. Order of convergence for the given numerical method is obtained. Numerical experiments are given to support theoretical results.eninfo:eu-repo/semantics/openAccessTerminal Value ProblemsSystems Of Fractional Differential EquationsExistenceRegularityWeakly Singular Volterra And Fredholm Integral EquationsPiecewise Polynomials Collocation MethodsArticle10.3934/math.20224202-s2.0-85124415544