Solvability of mixed Hilfer fractional functional boundary value problems with p-Laplacian at resonance

Abstract

Abstract This article investigates the existence of solutions of mixed Hilfer fractional differential equations with p-Laplacian under the functional boundary conditions at resonance. By defining Banach spaces with appropriate norms, constructing suitable operators, and using the extension of the continuity theorem, some of the current results are extended to the nonlinear situation, and some new existence results of the problem are obtained. Finally, an example is given to verify our main results.

Keywords

• Hilfer fractional derivative
• Functional boundary conditions
• Continuation theorem
• p-Laplacian
• Resonance