Abstract
In the commenced work, we establish some novel results concerning graph contractions in a more generalized setting. Furthermore, we deliver some examples to elaborate and explain the usability of the attained results. By virtue of nontrivial examples, we show our results improve, extend, generalize, and unify several noteworthy results in the existing state-of-art. We adopt computer simulation validating our results. To arouse further interest in the subject and to show its efficacy, we devote this work to recent applications which emphasize primarily the applications for the existence of the solution of various models related to engineering problems viz. fourth-order two-point boundary value problems describing deformations of an elastic beam, ascending motion of a rocket, and a class of integral equations. This approach is entirely new and will open up some new directions in the underlying graph structure.
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