{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T14:55:30Z","timestamp":1746802530000,"version":"3.40.5"},"reference-count":54,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,5,27]],"date-time":"2020-05-27T00:00:00Z","timestamp":1590537600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002383","name":"King Saud University","doi-asserted-by":"publisher","award":["RG-1441-326"],"award-info":[{"award-number":["RG-1441-326"]}],"id":[{"id":"10.13039\/501100002383","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2020,5,27]]},"abstract":"<jats:p>In this article, some new nonlinear fractional partial differential equations (PDEs) (the space-time fractional order Boussinesq equation; the space-time (2\u2009+\u20091)-dimensional breaking soliton equations; and the space-time fractional order SRLW equation) have been considered, in which the treatment of these equations in the diverse applications are described. Also, the fractional derivatives in the sense of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mi>\u03b2<\/mml:mi><\/mml:math>-derivative are defined. Some fractional PDEs will convert to consider ordinary differential equations (ODEs) with the help of transformation<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mi>\u03b2<\/mml:mi><\/mml:math>-derivative. These equations are analyzed utilizing an integration scheme, namely, the rational<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mi mathvariant=\"normal\">exp<\/mml:mi><mml:mfenced open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:mo>\u2212<\/mml:mo><mml:mi mathvariant=\"normal\">\u03a9<\/mml:mi><mml:mfenced open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:mi>\u03b7<\/mml:mi><\/mml:mrow><\/mml:mfenced><\/mml:mrow><\/mml:mfenced><\/mml:math>-expansion method. Different kinds of traveling wave solutions such as solitary, topological, dark soliton, periodic, kink, and rational are obtained as a by product of this scheme. Finally, the existence of the solutions for the constraint conditions is also shown. The outcome indicates that some fractional PDEs are used as a growing finding in the engineering sciences, mathematical physics, and so on.<\/jats:p>","DOI":"10.1155\/2020\/9179826","type":"journal-article","created":{"date-parts":[[2020,5,27]],"date-time":"2020-05-27T23:39:05Z","timestamp":1590622745000},"page":"1-22","source":"Crossref","is-referenced-by-count":1,"title":["Some Nonlinear Fractional PDEs Involving<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mi>\u03b2<\/mml:mi><\/mml:math>-Derivative by Using Rational<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mi mathvariant=\"normal\">exp<\/mml:mi><mml:mfenced open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:mo>\u2212<\/mml:mo><mml:mi mathvariant=\"normal\">\u03a9<\/mml:mi><mml:mfenced open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:mi>\u03b7<\/mml:mi><\/mml:mrow><\/mml:mfenced><\/mml:mrow><\/mml:mfenced><\/mml:math>-Expansion 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