Approximation approach to periodic BVP for fractional differential systems

Periodic boundary value problems for higher‐order fractional differential systems

“…The most reasonable alternative for FDS is to study periodic boundary value problem (PBVP) on finite intervals. In this paper, we continue our extension of a numerical‐analytic technique for ordinary differential equations suggested in previous works to the investigation of existence and approximate construction of solutions for FDS of the Caputo type of higher orders subjected to periodic boundary conditions. Then scalar FDE with asymptotically constant nonlinearities are investigated leading to Landesman‐Lazer–type conditions .…”

“…between matrixes and vectors are understood componentwise. Our aim is to establish a constructive method for solving FPBVP by following Feckan and Marynets . The assumptions (H1) to (H3) are natural conditions for applying a global Picard‐type iteration procedure with combination of a global Ljapunov‐Schmidt like decomposition, which is a basic idea of our method.…”

“…Our aim is to establish a constructive method for solving FPBVP (1), (2) by following Feckan and Marynets. 5,6 The assumptions (H1) to (H3) are natural conditions for applying a global Picard-type iteration procedure with combination of a global Ljapunov-Schmidt like decomposition, which is a basic idea of our method. Indeed, (H1) gives uniform boundedness and Lipschitzness of f. (H2) ensures that our iterations are located in the domain of definition D of f. Note…”

On One Interpolation Type Fractional Boundary-Value Problem

“…Since the approach of the numerical-analytic method [32] was appied to the fractional differential systems for the first time in [25][26][27][28], it is resonable to give an overview of the results that will allow the reader to follow and will open up possible perspectives for future research in this direction.…”

“…Recently, in the series of papers (see discussions [25][26][27][28]), a completely new approach for study of a class of fractional periodic and anti-periodic boundary-value problems was developed. To construct the approximate solutions of the studied problems, the numerical-analytic method, based on the successive iterations, was used.…”