{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T22:12:40Z","timestamp":1759702360196},"reference-count":15,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2012,8,15]],"date-time":"2012-08-15T00:00:00Z","timestamp":1344988800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Comput & Applic"],"published-print":{"date-parts":[[2013,11]]},"DOI":"10.1007\/s00521-012-1120-1","type":"journal-article","created":{"date-parts":[[2012,8,14]],"date-time":"2012-08-14T01:11:15Z","timestamp":1344906675000},"page":"1643-1647","source":"Crossref","is-referenced-by-count":10,"title":["A novel analytical solution of a fractional diffusion problem by homotopy analysis transform method"],"prefix":"10.1007","volume":"23","author":[{"given":"Muhammad Asif","family":"Godal","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ahmed","family":"Salah","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Majid","family":"Khan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Syeda Iram","family":"Batool","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2012,8,15]]},"reference":[{"key":"1120_CR1","volume-title":"An introduction to the fractional calculus and fractional differential equation","author":"KS Miller","year":"2003","unstructured":"Miller KS, Ross B (2003) An introduction to the fractional calculus and fractional differential equation. Willey, New York"},{"key":"1120_CR2","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1006\/jmaa.2000.7194","volume":"265","author":"K Diethelm","year":"2002","unstructured":"Diethelm K, Ford NJ (2002) Analysis of fractional differential equation. J Math Anal Appl 265:229\u2013248","journal-title":"J Math Anal Appl"},{"key":"1120_CR3","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1016\/0022-247X(76)90174-8","volume":"55","author":"G Adomian","year":"1976","unstructured":"Adomian G (1976) Nonlinear stochastic differential equations. J Math Anal Appl 55:441\u2013452","journal-title":"J Math Anal Appl"},{"key":"1120_CR4","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1016\/S0045-7825(99)00018-3","volume":"178","author":"JH He","year":"1999","unstructured":"He JH (1999) Homotopy perturbation technique. Comput Methods Appl Mech Eng 178:257\u2013262","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1120_CR5","doi-asserted-by":"crossref","DOI":"10.1201\/9780203491164","volume-title":"Beyond perturbation: introduction to the homotopy analysis methods","author":"SJ Liao","year":"2003","unstructured":"Liao SJ (2003) Beyond perturbation: introduction to the homotopy analysis methods. Chapman and Hall\/CRC Press, Boca Raton"},{"key":"1120_CR6","doi-asserted-by":"crossref","first-page":"1186","DOI":"10.1016\/j.amc.2004.10.058","volume":"169","author":"SJ Liao","year":"2005","unstructured":"Liao SJ (2005) Comparison between the homotopy analysis method and homotopy perturbation method. Appl Math Comput 169:1186\u20131194","journal-title":"Appl Math Comput"},{"key":"1120_CR7","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1016\/j.amc.2005.04.082","volume":"174","author":"S Saha Ray","year":"2006","unstructured":"Saha Ray S, Bera RK (2006) Analytical solution of a fractional diffusion equation by Adomian decomposition method. Appl Math Comput 174:329\u2013336","journal-title":"Appl Math Comput"},{"key":"1120_CR8","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1016\/j.camwa.2008.09.045","volume":"57","author":"S Das","year":"2009","unstructured":"Das S (2009) Analytical solution of a fractional diffusion equation by variational iteration method. Comput Math Appl 57:483\u2013487","journal-title":"Comput Math Appl"},{"key":"1120_CR9","doi-asserted-by":"crossref","first-page":"957","DOI":"10.1007\/BF02457955","volume":"19","author":"SJ Liao","year":"1998","unstructured":"Liao SJ (1998) Homotopy analysis method: a new analytic method for nonlinear problems. Appl Math Mech 19:957\u2013962","journal-title":"Appl Math Mech"},{"key":"1120_CR10","doi-asserted-by":"crossref","unstructured":"Salah A, Khan M, Gondal MA (2012) A novel solution procedure for fuzzy fractional heat equations by homotopy analysis transform method. Neural Comput Appl. doi: 10.1007\/s00521-012-0855-z","DOI":"10.1007\/s00521-012-0855-z"},{"key":"1120_CR11","doi-asserted-by":"crossref","first-page":"1143","DOI":"10.1016\/j.mcm.2011.09.038","volume":"55","author":"M Khan","year":"2012","unstructured":"Khan M, Gondal MA, Vanani SK (2012) A new comparative study between homotopy analysis transform method and homotopy perturbation transform method on a semi infinite. Math Comput Model 55:1143\u20131150","journal-title":"Math Comput Model"},{"key":"1120_CR12","unstructured":"Zurigat M (2011) Solving fractional oscillators using laplace homotopy analysis method. Annals Uni Craiova Math Comput Sci Ser 38(4):1\u201311"},{"key":"1120_CR13","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1016\/j.physleta.2006.02.048","volume":"355","author":"S Momani","year":"2006","unstructured":"Momani S, Odibat Z (2006) Analytical approach to linear fractional partial differential equations arising in fluid mechanics. Phys Lett A 355:271\u2013279","journal-title":"Phys Lett A"},{"key":"1120_CR14","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1016\/j.physleta.2007.05.002","volume":"369","author":"Z Odibat","year":"2007","unstructured":"Odibat Z, Momani S (2007) Numerical solution of Fokker\u2013Planck equation with space- and time-fractional derivatives. Phys Lett A 369:349\u2013358","journal-title":"Phys Lett A"},{"key":"1120_CR15","doi-asserted-by":"crossref","first-page":"4415","DOI":"10.1016\/j.camwa.2011.10.017","volume":"62","author":"A Charef","year":"2011","unstructured":"Charef A, Boucherma D (2011) Analytical solution of the linear fractional system of commensurate order. Comput Math Appl 62:4415\u20134428","journal-title":"Comput Math Appl"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-012-1120-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00521-012-1120-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-012-1120-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,28]],"date-time":"2019-05-28T22:14:45Z","timestamp":1559081685000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00521-012-1120-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,8,15]]},"references-count":15,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2013,11]]}},"alternative-id":["1120"],"URL":"https:\/\/doi.org\/10.1007\/s00521-012-1120-1","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,8,15]]}}}