Condensing Functions and Approximate Endpoint Criterion for the Existence Analysis of Quantum Integro-Difference FBVPs

A nonlinear quantum boundary value problem (q-FBVP) formulated in the sense of quantum Caputo derivative, with fractional q-integro-difference conditions along with its fractional quantum-difference inclusion q-BVP are investigated in this research. To prove the solutions' existence for these quantum systems, we rely on the notions such as the condensing functions and approximate endpoint criterion (AEPC). Two numerical examples are provided to apply and validate our main results in this research work.

Automated summary

In this research, a nonlinear quantum boundary value problem formulated in the sense of quantum Caputo derivative, along with fractional q-integro-difference conditions and its fractional quantum-difference inclusion q-BVP, are investigated. The existence of solutions for these quantum systems is proven using concepts such as condensing functions and the approximate endpoint criterion (AEPC). Two numerical examples are provided to validate the main results of this research.