On the parametrization of boundary-value problems with two-point nonlinear boundary conditions

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 .…”

Further results on the investigation of solutions of integral boundary value problems

“…Using this and arguing by induction according to Lemma 1 we can easily establish that 11) which means that all the functions (4.1) are also contained in the domain D,…”

“…To replace the boundary conditions (3.2) by certain linear two-point linear separated ones, similarly to [8]- [12], [14], [16], we apply a certain "freezing" technique. Namely, we introduce the vectors of parameters…”

“…According to the recurrence relation (3.12) of Lemma 2, using the Lipschitz condition (2.6) and the estimation (3.13), for m = 1 from (4.12) and (4.10) it follows that 14) where the matrix Q has the form (3.4). By induction we can easily establish that…”

The initial jumps of solutions and integral terms in singular BVP of linear higher order integro-differential equations

“…It is shown that there is the phenomenon of initial jumps not only of solutions, but also of the integral terms. The boundary-value problems were investigated in [16], [17] by using parametrization and the numerical analytic method based upon successive approximations [18].…”