{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:00:30Z","timestamp":1760241630609,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2018,6,27]],"date-time":"2018-06-27T00:00:00Z","timestamp":1530057600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>In this paper, two-dimensional Genocchi polynomials and the Ritz\u2013Galerkin method were developed to investigate the Fractional Diffusion Wave Equation (FDWE) and the Fractional Klein\u2013Gordon Equation (FKGE). A satisfier function that satisfies all the initial and boundary conditions was used. A linear system of algebraic equations was obtained for the considered equation with the help of two-dimensional Genocchi polynomials along with the Ritz\u2013Galerkin method. The FDWE and FKGE, including the nonlinear case, were reduced to solve the linear system of the algebraic equation. Hence, the proposed method was able to greatly reduce the complexity of the problems and provide an accurate solution. The effectiveness of the proposed technique is demonstrated through several examples.<\/jats:p>","DOI":"10.3390\/computation6030040","type":"journal-article","created":{"date-parts":[[2018,6,27]],"date-time":"2018-06-27T11:02:05Z","timestamp":1530097325000},"page":"40","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Numerical Solution of Fractional Diffusion Wave Equation and Fractional Klein\u2013Gordon Equation via Two-Dimensional Genocchi Polynomials with a Ritz\u2013Galerkin Method"],"prefix":"10.3390","volume":"6","author":[{"given":"Afshan","family":"Kanwal","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Universiti Tun Hussein Onn Malaysia, Pagoh Campus, 84600 Pagoh, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0291-3327","authenticated-orcid":false,"given":"Chang","family":"Phang","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Universiti Tun Hussein Onn Malaysia, Pagoh Campus, 84600 Pagoh, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Umer","family":"Iqbal","sequence":"additional","affiliation":[{"name":"Riphah College of Computing, Riphah International University, Faisalabad Campus, 38000 Faisalabad, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,6,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Povstenko, Y. 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