Generalized (ψ,φ)-contraction to investigate Volterra integral inclusions and fractal fractional PDEs in super-metric space with numerical experiments

Abstract

This article demonstrates the behavior of generalized (ψ,φ\psi ,\varphi )-type contraction mappings involving expressions of rational-type in the context of super-metric spaces. In this direction, we obtained unique and common fixed point results for a pair of mappings. The obtained results are then utilized to establish some corollaries. Moreover, numerical examples and applications related to the system of integral inclusions and fractal fractional partial differential equations have been presented to validate the established results. The central objective of this research is to provide a more comprehensive framework for generalizing classical results in the context of super-metric space.

Keywords

• positive solution
• fixed point
• fractional differential equation
• riemann-liouville fractional derivative
• existence and uniqueness
• 34a08
• 34a12
• 34b15