A study on advanced solutions for fractional integro-differential equations integrating Sawi transform and machine learning techniques

Document Type : Research Article

Authors

1 Department of Mathematics, Easwari Engineering College, 18 Bharathi Salai, Ramapuram Chennai-600089, Tamil Nadu, India Department of Mathematics and Science Education, Faculty of Education, Harran University, Sanliurfa, Turkey

2 Department of Mathematics, Vel Tech Rangarajan Dr.Sagunthala R&D Institute of Science and Technology, Avadi, Chennai, 600062, Tamil Nadu, India

Abstract

In this study, a direct method of fractional calculus approach to particular classes of fractional integro-differential equations is given. The method used reveals a number of interesting results most notably an extension of the familiar classical Frobenius' solution. The investigation is mainly based upon the basic results which are given to determine the fractional integro-differential equations by means of the Sawi transform and some extension coefficients defined from binomial series. Newer techniques for the efficient solution of these equations are also discussed and practical examples are used to demonstrate their use. In addition, we consider using a learning-based approach to improve the computation of our solution and illustrate how data-driven approaches can be used for obtaining approximate solutions in cases where analytical methods are not feasible or not efficient. The findings underscore the efficacy of combining classical and modern approaches in addressing complex fractional integro-differential equations.

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References

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Journal of Mathematical Modeling
Volume 14, Issue 3
August 2026
Pages 1147-1167

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