Related Experiment Video
Updated: Jun 28, 2025

Characterization of Thermal Transport in One-dimensional Solid Materials
Published on: January 26, 2014
Analytical solution of fuzzy heat problem in two-dimensional case under Caputo-type fractional derivative
Muhammad Nadeem1, Chen Yilin1, Devendra Kumar2
1School of Mathematics and Statistics, Qujing Normal University, Qujing, China.
Abstract:
This work aims to investigate the analytical solution of a two-dimensional fuzzy fractional-ordered heat equation that includes an external diffusion source factor. We develop the Sawi homotopy perturbation transform scheme (SHPTS) by merging the Sawi transform and the homotopy perturbation scheme. The fractional derivatives are examined in Caputo sense. The novelty and innovation of this study originate from the fact that this technique has never been tested for two-dimensional fuzzy fractional ordered heat problems. We presented two distinguished examples to validate our scheme, and the solutions are in fuzzy form. We also exhibit contour and surface plots for the lower and upper bound solutions of two-dimensional fuzzy fractional-ordered heat problems. The results show that this approach works quite well for resolving fuzzy fractional situations.
Related Concept Videos
Second Derivatives and Laplace Operator
Consider a scalar function. The curl of its...
Maxwell's Thermodynamic Relations
All thermodynamic potentials are exact differentials. Therefore, their second-order...
Heat Capacity: Problem-Solving
Determine the type of gas: The heat capacity of a gas depends on its molecular structure and the degree of freedom of its molecules. Different types of...
Conduction, Convection and Radiation: Problem Solving
In order to solve a problem related to heat transfer, first of all, the situation needs to be examined to determine the type of heat transfer involved. This could...
Dimensional Analysis
Linear Approximation in Frequency Domain
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....

