Existence results of nonlocal boundary value problem for a nonlinear fractional differential coupled system involving fractional order impulses

Abstract

In this paper, we study the nonlocal boundary value problem for a nonlinear fractional differential coupled system with fractional order impulses. Applying Nonlinear Alternative of Leray-Schauder, we obtain some new existence results for this system. As application, an interesting example is given to illustrate the effectiveness of our main result.

Coupled system of fractional differential equations with impulsive and nonlocal coupled boundary conditions

“…In particular, impulsive nonlocal boundary conditions are finite combinations of classical boundary problems and short-term perturbations whose duration can be negligible in comparison with the duration of the system process. They have advantages over classical boundary problems, because they can be used to model phenomena that cannot be modeled by traditional boundary problems; the reader can refer to [6,19] and references therein. The applications of many forms of fixed point theorems have been used extensively for investigations of existence and uniqueness problems of impulsive nonlocal fractional differential equations.…”

The Solutions of Some Riemann–Liouville Fractional Integral Equations

“…Using Lemma 1, Example 3 (iv), on (21) and denoting the Laplace transform L {y(t)} = Y(s), we obtain Y(s) = n!s 3σ (s − 1) n+1 (cs 3σ + bs 2σ + as σ + 1) . (22) For σ = 1/3, Equation (22) becomes…”