{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T14:30:05Z","timestamp":1774449005381,"version":"3.50.1"},"reference-count":52,"publisher":"Wiley","license":[{"start":{"date-parts":[[2022,7,20]],"date-time":"2022-07-20T00:00:00Z","timestamp":1658275200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Problems in Engineering"],"published-print":{"date-parts":[[2022,7,20]]},"abstract":"<jats:p>This paper presents a numerical method to solve accurately the fractional Black\u2013Scholes model of pricing evolution. A fully spectral collocation technique for the two independent variables is derived. The shifted fractional Jacobi\u2013Gauss\u2013Radau and shifted fractional Jacobi\u2013Gauss\u2013Lobatto collocation techniques are utilized. Firstly, the independent variables are interpolated at the shifted fractional Jacobi nodes, and the solution of the model is approximated by means of a sequence of shifted fractional Jacobi orthogonal functions. Then, the residuals at the shifted fractional Jacobi quadrature locations are estimated. As a result, an algebraic system of equations is obtained that can be solved using any appropriate approach. The accuracy of the proposed method is demonstrated using two numerical examples. It is observed that the new technique is more accurate, efficient, and feasible than other approaches reported in the literature. Indeed, the results show the exponential convergence of the method, both for smooth and nonsmooth solutions.<\/jats:p>","DOI":"10.1155\/2022\/9365292","type":"journal-article","created":{"date-parts":[[2022,7,20]],"date-time":"2022-07-20T23:50:30Z","timestamp":1658361030000},"page":"1-9","source":"Crossref","is-referenced-by-count":5,"title":["Spectral Solutions for Fractional Black\u2013Scholes Equations"],"prefix":"10.1155","volume":"2022","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9043-9644","authenticated-orcid":true,"given":"M. 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