Thanin SitthiwiratthamMuhammad ArfanKamal ShahAnwar ZebSalih DjilaliSaowaluck Chasreechai2025-03-102025-03-102021Fractal and Fractional2504311010.3390/fractalfract50401392-s2.0-85116477062https://repository.dusit.ac.th//handle/123456789/4690In the analysis in this article, we developed a scheme for the computation of a semi-analytical solution to a fuzzy fractional-order heat equation of two dimensions having some external diffusion source term. For this, we applied the Laplace transform along with decomposition tech-niques and the Adomian polynomial under the CaputoÐFabrizio fractional differential operator. Furthermore, for obtaining a semi-analytical series-type solution, the decomposition of the unknown quantity and its addition established the said solution. The obtained series solution was calculated and approached the approximate solution of the proposed equation. For the validation of our scheme, three different examples have been provided, and the solutions were calculated in fuzzy form. All the three illustrations simulated two different fractional orders between 0 and 1 for the upper and lower portions of the fuzzy solution. The said fractional operator is nonsingular and global due to the presence of the exponential function. It globalizes the dynamical behavior of the said equation, which is guaranteed for all types of fuzzy solution lying between 0 and 1 at any fractional order. The fuzziness is also included in the unknown quantity due to the fuzzy number providing the solution in fuzzy form, having upper and lower branches. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.All Open Access; Gold Open Access2D-fractional fuzzy heat equationCaputoÐFabrizio fractional operatorSemi-analytical solutionArticleScopus