Neutrosophic Sets and Systems
Abstract
This article uses the fractional residual power series (FRPS) method to solve a linear neutrosophic fractional integro-di erential equation in two dimensions. In what context does the term fractional derivative appeared, we presented the modi ed fractional power series method, a new technique that uses fractional power series expansion to approximate neutrosophic fractional integro-di erential equations. A modi ed new method has been formulated, which is an improvement on the RPS, named as Modi ed Fractional Power Series Method (MFPSM), to solve the same problem under investigation. Novel results associated with the rate of convergent and error order of the (MFPSM) was examined, and some ndings along with detailed proof were documented as theories. Several numerical examples are used to describe and test the validity and applicability of preset approaches. We investigate a semi-innite rod using the solution of our model, where heat transfer is inuenced by both the memory of past states and the current temperature distribution. The fractional derivative of order is used to represent memory e ects in heat transfer processes. To demonstrate the precision and e cacy of the two approaches, the results are shown in terms of tables and graphs. The modi ed fractional power series approach proved to be more e ective, e cient, and straightforward for solving the neutrosophic two-dimensional integro-di erential equations than the residual power series method, while also generating less error and computing time
Recommended Citation
Darweesh, Amer; Kamel Al- Khaled; Marwan Alquran; Adel Almalki; and Sohad Al-Omari. "Analytical Solutions of Heat Transfer Model in Two-Dimensional Case of Neutrosophic Fredholm Integro-Di erential Equations." Neutrosophic Sets and Systems 79, 1 (2025). https://digitalrepository.unm.edu/nss_journal/vol79/iss1/32
