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This research investigates specific classes of fractional integro-differential equations using a straightforward fractional calculus technique. The employed methodology yields a variety of compelling outcomes, including a generalized version of the well-established classical Frobenius method. The approach presented in this study primarily relies on fundamental theorems concerning the specific solutions of fractional integro-differential equations, utilizing the Mohand transform and binomial series extension coefficients. Additionally, advanced techniques for solving fractional integro-differential equations effectively are showcased. [ABSTRACT FROM AUTHOR]

In this article, the Upadhyaya transform is employed in diverse chemical reaction models expressed through ordinary differential equations. The investigation reveals that this transform provides precise and efficient solutions, circumventing the necessity for complex computations. Furthermore, the integration of graphical representations enhanced the interpretability of results, offering visual insights into the temporal evolution of reactant concentrations. These findings collectively underscore the efficacy of the Upadhyaya transform in addressing ordinary differential equations within chemical reaction models. [ABSTRACT FROM AUTHOR]

Background: Chemical graph theory has been used to mathematically model the various physical and biological aspects of chemical substances. A mathematical formulation that may be applied to any graph and can characterise a molecule structure is known as a topological index or molecular descriptor., Method: It is convenient and efficient to analyse the mathematical values and further research on various physical properties of a molecule based on these molecular descriptors. They provide useful alternatives to lengthy, expensive, and labour-intensive laboratory experiments. The topological indices can be used to predict the chemical structures, physicochemical properties, and biological activities using quantitative structure-activity relationships (QSARs) and quantitative structure-property relationships (QSPRs)., Result: In this study, the molecular descriptors of the Dodeca-benzo-circumcorenene compounds are derived based on their corresponding molecular structures., Conclusion: The computed indices are then compared graphically to study their relationship with the molecular structure and with each other.., (Copyright© Bentham Science Publishers; For any queries, please email at epub@benthamscience.net.)