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On nonlinear neutral Liouville-Caputo-type fractional differential equations with Riemann-Liouville integral boundary conditions

Ahmad Bashir, Ntouyas Sotiris K., Alsaedi Ahmed

Journal of Applied Analysis

2019

Vol. 25, nr 2

119--130

This paper studies neutral Liouville-Caputo-type fractional differential equations and inclusions supplemented with nonlocal Riemann-Liouville-type integral boundary conditions. Sadovskii’s fixed point theorem is applied to establish the existence result for the single-valued case, while the multivalued case is investigated by using nonlinear alternative for contractive maps. Examples are constructed to illustrate the main results. The case of nonlinear nonlocal boundary conditions is also discussed.

Oscillation criteria for higher order functional difference equation with oscillating coeffcient

Bolat Y.

Demonstratio Mathematica

2007

Vol. 40, nr 1

161-168

In this paper we are concerned with the oscillatory behaviour of solutions of a certain higher order nonlinear neutral type functional difference equation with oscillating coefficient. We obtain two sufficient criteria for oscillatory behaviour.