Decomposing Method for Space-Time Fractional Order PDEs : PDEs - Shukur, Ahmed; Jaber, Ahmed Shawki; RASHEED, MOHAMMED; Saidani, Tarek (Al-Salam Journal for Engineering and Technology, 2024)
Numerical solutions to integer-order differential equations frequently employ decomposition as one of many methods. This paper provides a generalization of integer-order differential equations into fractional order, which is more general, as well as generalizing the decomposing method into the fractional case and then applying it to solve differential equations of fractional order in both space and time. A fractional calculus's theorems and properties to generalize both differential equations and the decomposition method have been utilized. This method to solve different fractional time and space partial differential equations, demonstrating its ability and applicability to various problems have been applied. The method to various cases to highlight its strengths has been used. The graphs and tables of results obtained using Matlab programs have been presented and discussed.