Search

This study suggests a strategy for calculating the fuzzy analytical solutions to a two-dimensional fuzzy fractional-order heat problem including a diffusion variable connected externally. We propose Sawi residual power series scheme (SRPSS) which is the amalgamation of Sawi transform and residual power series scheme under the Caputo fractional differential operator. We demonstrate three different examples to derive the fuzzy fractional series solution which is characterized by its rapid convergence and easy finding of the unknown coefficients using the concept of limit at infinity. The most significant aspect of this scheme is that it derives the results without time effort compared with the traditional residual power series approach. Our findings confirm that the SRPSS is a robust and valuable method for approximating the solution of fuzzy fractional problems. Furthermore, we provide 2D and 3D symbolic representations to present the physical behavior of fuzzy fractional problems under the lower and upper bounded solutions. [ABSTRACT FROM AUTHOR]

This paper introduces a refined approach for obtaining the analytical solution of the nonlinear shock wave model incorporating fractal derivatives. The Fractal Yang Variational Iteration Strategy (FYVIS) is utilized to obtain the approximate solution of a fractal model in the form of a series under Caputo fractional operator. The suggested method is the composition of the fractal Yang transform and the variational iteration approach. By using the two-scale fractal theory, we transform the fractal model into its traditional problem and then apply the yang transform to generate a recurrence relation. The variational iteration approach is now suitable to handle this recurrence relation without imposing any hypotheses or restrictions on variables. The derived results by the proposed scheme are shown in terms of series solution. Numerical calculations verify the accuracy and consistency of the suggested approach, demonstrating its excellent performance. The dynamic behavior of fractal components is explored by evaluating absolute errors and presenting two-dimensional diagrams across the fractal domain. This investigation underscores that the suggested technique offers an efficient and user-friendly solution for solving the nonlinear shock wave model involving fractal derivatives. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The acquisition of agricultural land is a crucial aspect of survival for numerous rural communities, serving as a fundamental tool for combating poverty and food insecurity and promoting equitable sustainable economic progress. The expropriation of land offers a promising prospect for remedying past inequities and promoting both economic progress and food sufficiency. Limited research has examined the association between land expropriation and food security, livelihood shocks, and the well-being of rural households worldwide. Therefore, this research explores the implications of land expropriation on food security, livelihood shocks, and well-being of land lost rural communities. The data were collected from 384 farmers selected through stratified sampling techniques using face-to-face surveys in rural China. The data were analyzed using descriptive and logit regression models. The descriptive findings showed that land expropriation has detrimental effects on the livelihood, food security, and well-being of the farmers. Furthermore, these impacts are more harmful among land-expropriated households with a lower educational level, a large family size, and women farmers in less developed rural communities. The econometric results evinced that gender, age, education level, marital status, family size, and negative changes in income all significantly affect the impact of land expropriation on the food security of farmers. Similarly, the findings revealed that farmers with lower education levels were more likely to be affected by land loss as compared to farmers with medium and high education levels. Farmers with complete land loss were 1.70 times more likely to suffer livelihood shocks than those with partial land loss. The results also evinced that the well-being of all farmers was not affected equally, and some farmers' well-being was affected more than others due to various socioeconomic backgrounds. Therefore, this study suggests the implementation of public policies that provide support to farmers who have been marginalized due to land acquisition. [ABSTRACT FROM AUTHOR]