This paper derives a computationally efficient and fast-running solver for the approximate solution of fractional differential equations with impulsive effects. In this connection, for approximating the fractional-order integral operator, a B-spline version of interpolation by corresponding equal mesh points is adopted. An illustrative example illustrates the accuracy of the new solver results as compared with those of the previous study. The proposed solver’s performance is evaluated by the fractional Rössler and susceptible-exposed-infectious impulsive systems. Moreover, the effect of impulsive behaviors is shown for various values of impulsive.

/pdf/an-efficient-and-robust-numerical-solver-for-impulsive-3ses1898.pdf

An Efficient and Robust Numerical Solver for Impulsive Control of Fractional Chaotic Systems

In this paper, we are mainly concerned with existence of positive solutions for periodic boundary value problem of second-order impulsive differential equation with derivative in the nonlinearity $$\begin{aligned} \left\{ \begin{array}{ll} -u''+\rho ^{2} u=f(t, u, u'), &{} t \in J', \\ -\left. \Delta u'\right| _{t=t_{k}}=I_{k}(u(t_{k})), &{} k=1,2, \ldots m, \\ u(0)=u(2\pi ),\quad u^{\prime }(0)=u^{\prime }(2\pi ), &{} \end{array}\right. \end{aligned}$$
 where $$f:[0,2 \pi ] \times {\mathbb {R}}^{+} \times {\mathbb {R}} \rightarrow {\mathbb {R}}^{+}$$
 is continuous, $${\mathbb {R}}^{+}=[0,+\infty )$$
 , $$J=[0,2 \pi ]$$
 , $$ \rho >0$$
 , $$J^{\prime }=J \backslash \left\{ t_{1}, t_{2}, \ldots t_{m}\right\} .$$
 Some inequality conditions on nonlinearity f and the spectral radius condition of linear operator are presented that guarantee the existence of positive solution to the problem by the theory of fixed point index. The conditions allow that $$f\left( t, x_{1},x_{2}\right) $$
 has superlinear or sublinear growth in $$x_{1}, x_{2}$$
 .

Existence of positive solutions for periodic boundary value problems of second-order impulsive differential equation with derivative in the nonlinearity

In this paper, we are concerned with the existence, nonexistence, and multiplicity of positive solutions for a impulsive periodic boundary value problem with positive parameter λ$$ \lambda $$ . Using the critical point theorem, we obtain a bifurcation type result about positive solutions; that is, there exists 0Λ$$ \lambda >\Lambda $$ under the appropriate conditions.

Bifurcation type phenomena for positive solutions of a class of impulsive differential equations

The existence of positive periodic solutions for a class of second order impulsive differential equations is studied. By using a fixed point theorem in cone, we obtain two existence results, which extend some known results.

/pdf/positive-periodic-solutions-for-second-order-differential-18in5hxjn1.pdf

Positive periodic solutions for second order differential equations with impulsive effects

We study solvability of nonlocal boundary value problems for second-order differential equations with resonance or non-resonance. The method of proof relies on Schauder’s fixed point theorem. Some examples are presented to illustrate the main results. MSC: 34B05

/pdf/nonlocal-boundary-value-problems-with-resonant-or-non-4d2jqfol3g.pdf

Weibing Wang

Papers

Positive periodic solutions for second order differential equations with impulsive effects

Nonlocal boundary value problems with resonant or non-resonant conditions