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Then, we treat with various linear and nonlinear TFPDEs, among them, the space-tempered fractional advection and diffusion problem, the time-space tempered fractional advection\u2013diffusion problem (TFADP), the multi-term time-space tempered fractional problems, and the time-space tempered fractional Burgers\u2019 equation (TFBE) to investigate the numerical capability of the fractional collocation method. The study includes a numerical examination of the produced condition number <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\kappa (A)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>\u03ba<\/mml:mi>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mi>A<\/mml:mi>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> of the linear systems. The accuracy and efficiency of the proposed method are studied from the standpoint of the <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^\\infty $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mi>L<\/mml:mi>\n                    <mml:mi>\u221e<\/mml:mi>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-norm error and exponential rate of spectral convergence.<\/jats:p>","DOI":"10.1007\/s40314-023-02475-8","type":"journal-article","created":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T13:02:54Z","timestamp":1697720574000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["High-order spectral collocation method using tempered fractional Sturm\u2013Liouville eigenproblems"],"prefix":"10.1007","volume":"42","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5008-1174","authenticated-orcid":false,"given":"Sayed A.","family":"Dahy","sequence":"first","affiliation":[]},{"given":"H. 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