The study presents a meshless computational approach for simulating the three-dimensional multi-term time-fractional mobile-immobile diffusion equation in the Caputo sense. The methodology combines a stable Crank-Nicolson time-integration scheme with the definition of the Caputo derivative to discretize the problem in the temporal direction. The spatial function derivative is approximated using the inverse multiquadric radial basis function. The solution is approximated on a set of scattered or uniform nodes, resulting in a sparse and well-conditioned coefficient matrix. The study highlights the advantages of meshless method, particularly their simplicity of implementation in higher dimensions. To validate the accuracy and efficacy of the proposed method, we performed numerical simulations and compared them with analytical solutions for various test problems. These simulations were carried out on computational domains of both rectangular and non-rectangular shapes. The research highlights the potential of meshless techniques in solving complex diffusion problems and its successful applications in groundwater contamination and other relevant fields.
The extracts of E. alte offer promising potential as renewable resources for various chemical derivative products aimed at addressing antibiotic resistance. These extracts exhibited significant activity against methicillin-resistant Staphylococcus aureus (MRSA), a strain known for its resistance to multiple antibiotics. The extracts were found to be effective against several common antibiotics, including Imipenem, Ampicillin, Penicillin G, Oxacillin, and Amoxicillin-clavulanate. GC-MS analysis revealed that the phytoconstituents of E. alte extracts, obtained using both methanol and ethyl acetate, consist of a diverse range of 83 and 160 phytocompounds, respectively. These organic compounds serve as important biochemical precursors for the synthesis of vitamins E and K1, and exhibit antioxidant, antimicrobial, and anti-inflammatory properties in both plants and microorganisms. Notable compounds identified include fatty acids (such as palmitic acid, dodecanoic acid, sebacic acid, pentadecanoic acid, myristic acid, stearic acid, behenic acid, and linoelaidic acid), phytosterols (Campesterol, β-sitosterol, Stigmast-5-ene), sugars (D-fructose, Fructofuranans), terpenoids (Phytol, citronellol), and phenolic acids (Protocatechoic acid, shikimic acid). The antimicrobial activity of all E. alte extracts was found to be superior to that of mupirocin and ciprofloxacin, as observed in susceptibility testing against MRSA ATCC 43300 and other pathogenic bacteria and fungi. It is likely that the combined action of the antimicrobial components within the E. alte extract bypasses the mechanisms employed by MRSA to protect itself from antibiotics. Further experiments are needed to investigate the individual effects of each pure compound and their potential synergistic interactions, which may enhance their overall performance.