Study of Fractional Differential Equations Emerging in the Theory of Chemical Graphs: A Robust Approach

Abstract

The study of the interconnections between chemical systems is known as chemical graph theory. Through the use of star graphs, a limited group of researchers has examined the space of possible solutions for boundary-value problems. They recognized that for their strategy to function, they needed a core node related to other nodes but not to itself; as a result, they opted to use star graphs. In this sense, the graphs of neopentane will be helpful in extending the scope of our technique. It has the CAS number 463-82-1 and the chemical formula C5H12, and it is a component of a petrochemical precursor. In order to determine whether or not the suggested boundary-value problems on these graphs have any known solutions, we use the theorems developed by Schaefer and Krasnoselskii on fixed points. In addition, we illustrate our preliminary results with the help of an example that we present.

Fixed Point Method for Nonlinear Fractional Differential Equations with Integral Boundary Conditions on Tetramethyl-Butane Graph

“…Recently, Wajahat Ali et al [26] discussed the novel existence result for an FDE on a graph of cyclohexane. For more studies on graphs, one can refer to [27][28][29][30][31][32][33][34][35].…”

Smoothing and differentiation of data by Tikhonov and fractional derivative tools, applied to surface‐enhanced Raman scattering (SERS) spectra of crystal violet dye

“…Fractional calculus is a branch of mathematical analysis that generalizes the derivatives and integrals of integer order as arbitrary order. Although the history of fractional calculus started almost simultaneously to its integer‐order counterpart, the mathematics, and especially its applications, are considerably less developed and recently has received more attention from chemists 34–38 . Of the many definitions for fractional‐order derivative, the GL definition is the most often used 27 .…”

“…Although the history of fractional calculus started almost simultaneously to its integer-order counterpart, the mathematics, and especially its applications, are considerably less developed and recently has received more attention from chemists. [34][35][36][37][38] Of the many definitions for fractional-order derivative, the GL definition is the most often used. 27 The GL definition is simply a generalization of the ordinary discretization formula for integer order derivatives, and most straightforward from the point of view of numerical implementation.…”