{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T02:01:55Z","timestamp":1771466515117,"version":"3.50.1"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2022,3,4]],"date-time":"2022-03-04T00:00:00Z","timestamp":1646352000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,3,4]],"date-time":"2022-03-04T00:00:00Z","timestamp":1646352000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2022,4]]},"DOI":"10.1007\/s40314-022-01802-9","type":"journal-article","created":{"date-parts":[[2022,3,4]],"date-time":"2022-03-04T16:45:54Z","timestamp":1646412354000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Generalized Mellin transform and its applications in fractional calculus"],"prefix":"10.1007","volume":"41","author":[{"given":"Talha","family":"Aziz","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2511-8622","authenticated-orcid":false,"given":"Mujeeb ur","family":"Rehman","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,3,4]]},"reference":[{"key":"1802_CR1","doi-asserted-by":"publisher","first-page":"460","DOI":"10.1016\/j.cnsns.2016.09.006","volume":"44","author":"R Almeida","year":"2017","unstructured":"Almeida R (2017) A Caputo fractional derivative of a function with respect to another function. Commun Nonlinear Sci Numer Simul 44:460\u201381","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"1802_CR2","unstructured":"Arran F, Joel R, Jean-Daniel D (2021) On the fractional Laplacian of a function with respect to another function. hal-03318401"},{"key":"1802_CR3","doi-asserted-by":"crossref","unstructured":"Atangana A, Bildik N (2013) The use of fractional order derivative to predict the groundwater flow. Math Probl Eng 2013","DOI":"10.1186\/1687-2770-2013-53"},{"issue":"1","key":"1802_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0022-247X(02)00001-X","volume":"269","author":"PL Butzer","year":"2002","unstructured":"Butzer PL, Kilbas AA, Trujillo JJ (2002) Fractional calculus in the Mellin setting and Hadamard-type fractional integrals. J Math Anal Appl 269(1):1\u201327","journal-title":"J Math Anal Appl"},{"issue":"1","key":"1802_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0022-247X(02)00066-5","volume":"270","author":"PL Butzer","year":"2002","unstructured":"Butzer PL, Kilbas AA, Trujillo JJ (2002) Mellin transform analysis and integration by parts for Hadamard-type fractional integrals. J Math Anal Appl 270(1):1\u20135","journal-title":"J Math Anal Appl"},{"key":"1802_CR6","doi-asserted-by":"publisher","DOI":"10.1201\/9781420010916","volume-title":"Integral transforms and their applications","author":"L Debnath","year":"2016","unstructured":"Debnath L, Bhatta D (2016) Integral transforms and their applications. Chapman and Hall\/CRC, New York"},{"key":"1802_CR7","series-title":"Lecture notes in mathematics.","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-14574-2","volume-title":"The analysis of fractional differential equations","author":"K Diethelm","year":"2010","unstructured":"Diethelm K (2010) The analysis of fractional differential equations. Lecture notes in mathematics. Springer, Berlin"},{"key":"1802_CR8","doi-asserted-by":"publisher","DOI":"10.1201\/9781420035148","volume-title":"Transform methods for solving partial differential equations","author":"DG Duffy","year":"2004","unstructured":"Duffy DG (2004) Transform methods for solving partial differential equations. Chapman and Hall\/CRC, New York"},{"key":"1802_CR9","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1137\/0112002","volume":"1","author":"A Erd\u00e9lyi","year":"1964","unstructured":"Erd\u00e9lyi A (1964) An integral equation involving Legendre functions. J Soc Ind Appl Math 1:15\u201330","journal-title":"J Soc Ind Appl Math"},{"key":"1802_CR10","unstructured":"Fahad HM, Fernandez A (2019) On Laplace transforms with respect to functions and their applications to fractional differential equations. arXiv preprint arXiv:1907.04541"},{"issue":"4","key":"1802_CR11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00009-021-01783-9","volume":"18","author":"HM Fahad","year":"2021","unstructured":"Fahad HM, Fernandez A, Rehman M, Siddiqi M (2021) Tempered and Hadamard-type fractional calculus with respect to functions. Mediterr J Math 18(4):1\u201328","journal-title":"Mediterr J Math"},{"issue":"1","key":"1802_CR12","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1007\/BF02422942","volume":"41","author":"GH Hardy","year":"1916","unstructured":"Hardy GH, Littlewood JE (1916) Contributions to the theory of the Riemann zeta-function and the theory of the distribution of primes. Acta Math 41(1):119\u201396","journal-title":"Acta Math"},{"key":"1802_CR13","doi-asserted-by":"crossref","unstructured":"Hilfer R (2000) editor. Applications of fractional calculus in physics. World scientific","DOI":"10.1142\/3779"},{"issue":"3","key":"1802_CR14","first-page":"709","volume":"13","author":"F Jarad","year":"2020","unstructured":"Jarad F, Abdeljawad T (2020) Generalized fractional derivatives and Laplace transform. Discrete Contin Dyn Syst 13(3):709","journal-title":"Discrete Contin Dyn Syst"},{"issue":"3","key":"1802_CR15","first-page":"860","volume":"218","author":"UN Katugampola","year":"2011","unstructured":"Katugampola UN (2011) New approach to a generalized fractional integral. Appl Math Comput 218(3):860\u20135","journal-title":"Appl Math Comput"},{"key":"1802_CR16","first-page":"566","volume":"257","author":"UN Katugampola","year":"2015","unstructured":"Katugampola UN (2015) Mellin transforms of generalized fractional integrals and derivatives. Appl Math Comput 257:566\u201380","journal-title":"Appl Math Comput"},{"key":"1802_CR17","unstructured":"Kenneth S (1993) Miller, Bertram Ross, An introduction to the fractional calculus and fractional differential equations. New York. Wiley"},{"key":"1802_CR18","unstructured":"Kilbas AA (2001) Hadamard-type fractional calculus. J Korean Math Soc 38"},{"key":"1802_CR19","unstructured":"Kilbas AA, Srivastava HM, Trujillo JJ (2006) Theory and applications of fractional differential equations. North-Holland mathematics studies, 204. Amsterdam: Elsevier Science B.V"},{"issue":"1","key":"1802_CR20","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s40064-016-1711-x","volume":"5","author":"A K\u0131l\u0131\u00e7man","year":"2016","unstructured":"K\u0131l\u0131\u00e7man A, Omran M (2016) Note on fractional Mellin transform and applications. Springerplus 5(1):1\u20138","journal-title":"Springerplus"},{"issue":"2","key":"1802_CR21","doi-asserted-by":"publisher","first-page":"288","DOI":"10.1137\/0501026","volume":"1","author":"TJ Osler","year":"1970","unstructured":"Osler TJ (1970) The fractional derivative of a composite function. SIAM J Math Anal 1(2):288\u201393","journal-title":"SIAM J Math Anal"},{"key":"1802_CR22","volume-title":"Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications","author":"I Podlubny","year":"1998","unstructured":"Podlubny I (1998) Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Elsevier, Amsterdam"},{"key":"1802_CR23","doi-asserted-by":"publisher","DOI":"10.1201\/9781420011494","volume-title":"Operational calculus and related topics","author":"AP Prudnikov","year":"2006","unstructured":"Prudnikov AP (2006) Operational calculus and related topics. Chapman and Hall\/CRC, New York"},{"key":"1802_CR24","volume-title":"Fractional integrals and derivatives, translated from the 1987 Russian original","author":"SG Samko","year":"1993","unstructured":"Samko SG, Kilbas AA, Marichev OI (1993) Fractional integrals and derivatives, translated from the 1987 Russian original. Gordon and Breach, Yverdon"},{"key":"1802_CR25","doi-asserted-by":"crossref","unstructured":"Sousa JV, da C., Capelas De Oliveira E (2019) Leibniz type rule: $$\\psi $$-Hilfer fractional operator. Commun Nonlinear Sci Numer Simul 77:305\u2013311","DOI":"10.1016\/j.cnsns.2019.05.003"},{"key":"1802_CR26","doi-asserted-by":"publisher","first-page":"72","DOI":"10.1016\/j.cnsns.2018.01.005","volume":"60","author":"J Sousa","year":"2018","unstructured":"Sousa J, da Vanterler C, Capelas De Oliveira E (2018) On the $$\\psi $$-Hilfer fractional derivative. Commun Nonlinear Sci Numer Simul 60:72\u201391","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"1802_CR27","volume-title":"Fractional dynamics: applications of fractional calculus to dynamics of particles, fields and media","author":"VE Tarasov","year":"2011","unstructured":"Tarasov VE (2011) Fractional dynamics: applications of fractional calculus to dynamics of particles, fields and media. Springer, New York"},{"issue":"10","key":"1802_CR28","doi-asserted-by":"publisher","first-page":"1377","DOI":"10.1016\/j.advwatres.2008.07.004","volume":"31","author":"SW Wheatcraft","year":"2008","unstructured":"Wheatcraft SW, Meerschaert MM (2008) Fractional conservation of mass. Adv Water Resour 31(10):1377\u201381","journal-title":"Adv Water Resour"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-022-01802-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-022-01802-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-022-01802-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,18]],"date-time":"2022-04-18T18:52:01Z","timestamp":1650307921000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-022-01802-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,4]]},"references-count":28,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2022,4]]}},"alternative-id":["1802"],"URL":"https:\/\/doi.org\/10.1007\/s40314-022-01802-9","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,3,4]]},"assertion":[{"value":"12 September 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 February 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 February 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 March 2022","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"88"}}