Analytical Solutions of Heat Transfer Model in Two-Dimensional Case of Neutrosophic Fredholm Integro-Di erential Equations

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.

DOI: 10.5281/zenodo.14597586