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It has been demonstrated that the Laplace transform is an excellent choice for solving diffusion problems and offers a substitute to the finite difference approach. In this paper, a method based on Laplace transform coupled with the pseudospectral method was developed for the novel model. The proposed method has three main steps: First, the model was reduced to a time-independent model via Laplace transform; second, the pseudospectral method was employed for spatial discretization; and finally, the inverse Laplace transform was applied to transform the obtained solution in Laplace transform domain back into a real domain. We also presented the numerical scheme's stability and convergence analysis. To demonstrate our method's efficacy, four problems were examined.&lt;\/p&gt;&lt;\/abstract&gt;<\/jats:p>","DOI":"10.3934\/nhm.2024003","type":"journal-article","created":{"date-parts":[[2024,1,15]],"date-time":"2024-01-15T12:12:45Z","timestamp":1705320765000},"page":"44-85","source":"Crossref","is-referenced-by-count":9,"title":["Application of a hybrid pseudospectral method to a new two-dimensional multi-term mixed sub-diffusion and wave-diffusion equation of fractional order"],"prefix":"10.3934","volume":"19","author":[{"given":"Farman Ali","family":"Shah","sequence":"first","affiliation":[{"name":"Department of Mathematics, Islamia College Peshawar, Jamrod Road, Peshawar 25120, Khyber PakhtunKhwa, Pakistan"}]},{"family":"Kamran","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Islamia College Peshawar, Jamrod Road, Peshawar 25120, Khyber PakhtunKhwa, Pakistan"}]},{"given":"Dania","family":"Santina","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"}]},{"given":"Nabil","family":"Mlaiki","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"}]},{"given":"Salma","family":"Aljawi","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Princess Nourah Bint Abdulrahman University, Riyadh, PO Box 84428, Saudi Arabia"}]}],"member":"2321","reference":[{"key":"key-10.3934\/nhm.2024003-1","doi-asserted-by":"publisher","unstructured":"R. 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