Solvability Analysis of (k − ℓ)-Hilfer Fractional Differential Equations through Generalized Weak Wardowski Contractions

Abstract

In this work, we introduce the concept of generalized weak Wardowski contractions and establish the existence and uniqueness of fixed points for such mappings. Furthermore, we apply weak Wardowski contraction to investigate the existence of solutions for a novel (k − ℓ)-Hilfer fractional differential equation of order 2 < α ≤ 3 subject to specific boundary conditions. Finally, an example is provided to illustrate the applicability and effectiveness of the obtained theoretical results.