New Multiplicity Results for a Boundary Value Problem Involving a <i>ψ</i>-Caputo Fractional Derivative of a Function with Respect to Another Function

Abstract

This paper considers a nonlinear impulsive fractional boundary value problem, which involves a ψ-Caputo-type fractional derivative and integral. Combining critical point theory and fractional calculus properties, such as the semigroup laws, and relationships between the fractional integration and differentiation, new multiplicity results of infinitely many solutions are established depending on some simple algebraic conditions. Finally, examples are also presented, which show that Caputo-type fractional models can be more accurate by selecting different kernels for the fractional integral and derivative.

Keywords

• critical point theory
• differential equation
• <i>ψ</i>-Caputo fractional operator
• infinitely many solutions