{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T23:52:27Z","timestamp":1771631547067,"version":"3.50.1"},"reference-count":27,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Model. Simul. Sci. Comput."],"published-print":{"date-parts":[[2022,2]]},"abstract":"<jats:p> This article introduces the computational analytical approach to solve the m-dimensional space-time variable Caputo fractional order advection\u2013dispersion equation with the Dirichlet boundary using the two-step Adomian decomposition method and obtain the exact solution in just one iteration. Moreover, with the help of fixed point theory, we study the existence and uniqueness conditions for the positive solution and prove some new results. Also, obtain the Ulam\u2013Hyers stabilities for the proposed problem. Two generalized examples are considered to show the method\u2019s applicability and compared with other existing numerical methods. The present method performs exceptionally well in terms of efficiency and simplicity. Further, we solved both examples using the two most well-known numerical methods and compared them with the TSADM solution. <\/jats:p>","DOI":"10.1142\/s1793962322500040","type":"journal-article","created":{"date-parts":[[2021,8,31]],"date-time":"2021-08-31T10:38:56Z","timestamp":1630406336000},"source":"Crossref","is-referenced-by-count":8,"title":["Ulam\u2013Hyers stability and analytical approach for m-dimensional Caputo space-time variable fractional order advection\u2013dispersion equation"],"prefix":"10.1142","volume":"13","author":[{"given":"Pratibha","family":"Verma","sequence":"first","affiliation":[{"name":"Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Prayagraj\u2013211004, Uttar Pradesh, India"}]},{"given":"Manoj","family":"Kumar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Prayagraj\u2013211004, Uttar Pradesh, India"}]},{"given":"Anand","family":"Shukla","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Wollega University, Nekemte, Ethiopia"}]}],"member":"219","published-online":{"date-parts":[[2021,8,31]]},"reference":[{"key":"S1793962322500040BIB001","first-page":"4352357","volume":"2020","author":"Abdeljawad T.","year":"2020","journal-title":"J. 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