On Impulsive Boundary Value Problem with Riemann-Liouville Fractional Order Derivative

Our manuscript is devoted to investigating a class of impulsive boundary value problems under the concept of the Riemann-Liouville fractional order derivative. The subject problem is of implicit type. We develop some adequate conditions for the existence and puniness of a solution to the proposed problem. For our required results, we utilize the classical fixed point theorems from Banach and Scheafer. It is to be noted that the impulsive boundary value problem under the fractional order derivative of the Riemann-Liouville type has been very rarely considered in literature. Finally, to demonstrate the obtained results, we provide some pertinent examples.

Semi-nonoscillation intervals and sign-constancy of Green’s functions of two-point impulsive boundary-value problems

UDC 517.9 We consider the second order impulsive differential equation with delays where for In this paper, we obtain the conditions of semi-nonoscillation for the corresponding homogeneous equation on the interval Using these results, we formulate theorems on sign-constancy of Green's functions for two-point impulsive boundary-value problems in terms of differential inequalities.

Investigation of solutions of state-dependent multi-impulsive boundary value problems

We describe a reduction technique allowing one to combine an analysis of the existence of solutions with an efficient construction of approximate solutions for a state-dependent multi-impulsive boundary value problem which consists of non-linear system of differential equationsu^{\prime}(t)=f(t,u(t))\quad\text{for a.e. }t\in[a,b],subject to the state-dependent impulse conditionu(t+)-u(t-)=\gamma_{t}(u(t-))\quad\text{for }t\in(a,b)\text{ such that }g(t,u(% t-))=0,and the non-linear two-point boundary conditionV(u(a),u(b))=0.