Solvability of Nonlinear Impulsive Generalized Fractional Differential Equations with (<i>p</i>,<i>q</i>)-Laplacian Operator via Critical Point Theory

Abstract

In this paper, we consider the nonlinear impulsive generalized fractional differential equations with (p,q)-Laplacian operator for 1p≤q∞, in which the nonlinearity f contains two fractional derivatives with respect to another function. Since the complexity of the nonlinear term and the impulses exist in generalized fractional calculus, it is difficult to find the corresponding variational functional of the problem. The existence of nontrivial solutions for the problem is established by the mountain pass theorem and iterative technique under some appropriate assumptions. Furthermore, our main result is demonstrated by an illustrative example to show its feasibility and effectiveness. Due to the employment of a generalized fractional operator, our results extend some existing research findings.

Keywords

• (<i>p</i>,<i>q</i>)-Laplacian operator
• generalized fractional differential operator
• mountain pass theorem
• impulse