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The utilization of time-fractional PDEs in diverse fields within science and technology has attracted significant interest from researchers. This paper presents a relatively new numerical approach aimed at solving two-term time-fractional PDE models in two and three dimensions. We combined the Liouville–Caputo fractional derivative scheme with the Strang splitting algorithm for the temporal component and employed a meshless technique for spatial derivatives utilizing Lucas and Fibonacci polynomials. The rising demand for meshless methods stems from their inherent mesh-free nature and suitability for higher dimensions. Moreover, this approach demonstrates the effective approximation of solutions across both regular and irregular domains. Error norms were used to assess the accuracy of the methodology across both regular and irregular domains. A comparative analysis was conducted between the exact solution and alternative numerical methods found in the contemporary literature. The findings demonstrate that our proposed approach exhibited better performance while demanding fewer computational resources. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence of at least two weak solutions to a class of singular two-phase problems with variable exponents involving a ψ-Hilfer fractional operator and Dirichlet-type boundary conditions when the term source is dependent on one parameter. Here, we use the fiber method and the Nehari manifold to prove our results. [ABSTRACT FROM AUTHOR]