Approximation of solutions of fractional differential systems (FDS) of higher orders is studied for periodic boundary value problem (PBVP). We propose a numerical‐analytic technique to construct a sequence of functions convergent to the limit function, which is a solution of the given PBVP, if the corresponding determined equation has a root. We also study scalar fractional differential equations (FDE) with asymptotically constant nonlinearities leading to Landesman‐Lazer–type conditions.
ABSTRACT. We give a new approach for the investigation of existence and construction of an approximate solutions of nonlinear non-autonomous systems of ordinary differential equations under nonlinear integral boundary conditions depending on the derivative. The constructivity of a suggested technique is shown on the example of non-linear integral boundary value problem with two solutions.
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