{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T05:54:55Z","timestamp":1773813295361,"version":"3.50.1"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2024,4,1]],"date-time":"2024-04-01T00:00:00Z","timestamp":1711929600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,4,1]],"date-time":"2024-04-01T00:00:00Z","timestamp":1711929600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2024,4]]},"DOI":"10.1007\/s40314-024-02681-y","type":"journal-article","created":{"date-parts":[[2024,4,2]],"date-time":"2024-04-02T20:25:04Z","timestamp":1712089504000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["On existence of solutions for $$\\Psi $$-Hilfer type fractional BVP of generalized higher order"],"prefix":"10.1007","volume":"43","author":[{"family":"Bhupeshwar","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Deepesh Kumar","family":"Patel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Moosa","family":"Gabeleh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5450-3127","authenticated-orcid":false,"given":"Mohammad Esmael","family":"Samei","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,4,2]]},"reference":[{"key":"2681_CR1","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1155\/2009\/494720","volume":"2009","author":"B Ahmad","year":"2009","unstructured":"Ahmad B, Nieto JJ (2009) Existence of solutions for nonlocal boundary value problems of higher-order nonlinear fractional differential equations. Abstr Appl Anal 2009:9. https:\/\/doi.org\/10.1155\/2009\/494720","journal-title":"Abstr Appl Anal"},{"issue":"14","key":"2681_CR2","doi-asserted-by":"publisher","first-page":"4751","DOI":"10.2298\/FIL2214751A","volume":"36","author":"A Alsaedi","year":"2022","unstructured":"Alsaedi A, Assolami A, Ahmad B (2022) Existence results for nonlocal Hilfer-type integral-multipoint boundary value problems with mixed nonlinearities. Filomat 36(14):4751\u20134766. https:\/\/doi.org\/10.2298\/FIL2214751A","journal-title":"Filomat"},{"issue":"2","key":"2681_CR3","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2022.112822","volume":"165","author":"P Amiri","year":"2022","unstructured":"Amiri P, Samei ME (2022) Existence of Urysohn and Atangana\u2013Baleanu fractional integral inclusion systems solutions via common fixed point of multi-valued operators. Chaos Solitons Fractals 165(2):112822. https:\/\/doi.org\/10.1016\/j.chaos.2022.112822","journal-title":"Chaos Solitons Fractals"},{"issue":"6","key":"2681_CR4","doi-asserted-by":"publisher","first-page":"1639","DOI":"10.4134\/BKMS.b170887","volume":"55","author":"S Asawasamrit","year":"2018","unstructured":"Asawasamrit S, Kijjathanakorn A, Ntouyas SK, Tariboon J (2018) Nonlocal boundary value problems for Hilfer fractional differential equations. Bull Korean Math Soc 55(6):1639\u20131657. https:\/\/doi.org\/10.4134\/BKMS.b170887","journal-title":"Bull Korean Math Soc"},{"key":"2681_CR5","doi-asserted-by":"publisher","DOI":"10.1002\/9781118577530","volume-title":"Fractional calculus with applications in mechanics: vibrations and diffusion processes","author":"TM Atanackovic","year":"2014","unstructured":"Atanackovic TM, Pilipovic S, Stankovic B, Zorica D (2014) Fractional calculus with applications in mechanics: vibrations and diffusion processes. Wiley-ISTE, London"},{"key":"2681_CR6","doi-asserted-by":"publisher","first-page":"133","DOI":"10.4064\/fm-3-1-133-181","volume":"3","author":"S Banach","year":"1922","unstructured":"Banach S (1922) Sur les op\u00e9rations dans les ensembles abstraits et leur application aux equation int\u00e9grales. Fundam Math 3:133\u2013181","journal-title":"Fundam Math"},{"key":"2681_CR7","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1186\/s13662-022-03716-6","volume":"2022","author":"A Berhail","year":"2022","unstructured":"Berhail A, Tabouche N, Alzabut J, Samei ME (2022) Using Hilfer\u2013Katugampola fractional derivative in initial value Mathieu fractional differential equations with application on particle in the plane. Adv Contin Discrete Models Theory Appl 2022:44. https:\/\/doi.org\/10.1186\/s13662-022-03716-6","journal-title":"Adv Contin Discrete Models Theory Appl"},{"key":"2681_CR8","doi-asserted-by":"publisher","DOI":"10.1016\/j.padiff.2023.100495","volume":"7","author":"SP Bhairat","year":"2023","unstructured":"Bhairat SP, Samei ME (2023) Non-existence of a global solution for Hilfer\u2013Katugampola fractional differential problem. Partial Differ Equ Appl Math 7:100495. https:\/\/doi.org\/10.1016\/j.padiff.2023.100495","journal-title":"Partial Differ Equ Appl Math"},{"issue":"2","key":"2681_CR9","doi-asserted-by":"publisher","first-page":"538","DOI":"10.1685\/journal.caim.538","volume":"6","author":"F Costa","year":"2015","unstructured":"Costa F, Grigoletto EC, Vaz J, de Oliveira EC (2015) Slowing-down of neutrons: a fractional model. Commun Appl Ind Math 6(2):538. https:\/\/doi.org\/10.1685\/journal.caim.538","journal-title":"Commun Appl Ind Math"},{"key":"2681_CR10","doi-asserted-by":"publisher","unstructured":"Furati KM, Kassim M, Tatar Ne (2012) Existence and uniqueness for a problem involving Hilfer fractional derivative. Comput Math Appl 64(6):1616\u20131626. https:\/\/doi.org\/10.1016\/j.camwa.2012.01.009","DOI":"10.1016\/j.camwa.2012.01.009"},{"key":"2681_CR11","doi-asserted-by":"crossref","unstructured":"Furati KM, Tatar Kassim MD, NE, (2013) Non-existence of global solutions for a differential equation involving Hilfer fractional derivative. Electron J Differ Equ 235:1\u201310","DOI":"10.1155\/2012\/391062"},{"key":"2681_CR12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-43930-2","volume-title":"Mittag\u2013Leffler functions, related topics and applications","author":"R Gorenflo","year":"2014","unstructured":"Gorenflo R, Kilbas AA, Mainardi F, Rogosin SV (2014) Mittag\u2013Leffler functions, related topics and applications. Springer, Berlin"},{"key":"2681_CR13","volume-title":"Fixed point theory","author":"A Granas","year":"2005","unstructured":"Granas A, Dugundji J (2005) Fixed point theory. Springer, New York"},{"key":"2681_CR14","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1007\/s11868-023-00555-1","volume":"14","author":"F Haddouchi","year":"2023","unstructured":"Haddouchi F, Samei ME, Rezapour S (2023) Study of a sequential $$\\psi $$-Hilfer fractional integro-differential equations with nonlocal BCs. J Pseudo Differ Oper Appl 14:61. https:\/\/doi.org\/10.1007\/s11868-023-00555-1","journal-title":"J Pseudo Differ Oper Appl"},{"key":"2681_CR15","doi-asserted-by":"publisher","first-page":"1378","DOI":"10.1515\/math-2021-0093","volume":"19","author":"SN Hajiseyedazizi","year":"2021","unstructured":"Hajiseyedazizi SN, Samei ME, Alzabut J, Chu Y (2021) On multi-step methods for singular fractional $$q$$-integro-differential equations. Open Math 19:1378\u20131405. https:\/\/doi.org\/10.1515\/math-2021-0093","journal-title":"Open Math"},{"key":"2681_CR16","doi-asserted-by":"publisher","DOI":"10.1142\/8072","volume-title":"Fractional calculus: an introduction for physicists","author":"R Herrmann","year":"2011","unstructured":"Herrmann R (2011) Fractional calculus: an introduction for physicists. World Scientific Publishing Company, Amsterdam"},{"key":"2681_CR17","volume-title":"Application of fractional calculus in physics","author":"R Hilfer","year":"1999","unstructured":"Hilfer R (1999) Application of fractional calculus in physics. World Scientific, Singapore"},{"issue":"3","key":"2681_CR18","first-page":"299","volume":"12","author":"R Hilfer","year":"2009","unstructured":"Hilfer R, Luchko Y, Tomovski V (2009) Operational method for the solution of fractional differential equations with generalized Riemann\u2013Lioville fractional derivative. Fract Calc Appl Anal 12(3):299\u2013318","journal-title":"Fract Calc Appl Anal"},{"issue":"4","key":"2681_CR19","doi-asserted-by":"publisher","first-page":"1938","DOI":"10.1002\/mma.6017","volume":"43","author":"JP Kharade","year":"2019","unstructured":"Kharade JP, Kucche KD (2019) On the impulsive implicit $$\\psi $$-Hilfer fractional differential equations with delay. Math Methods Appl Sci 43(4):1938\u20131952. https:\/\/doi.org\/10.1002\/mma.6017","journal-title":"Math Methods Appl Sci"},{"issue":"1","key":"2681_CR20","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2022.113007","volume":"166","author":"T Kherraz","year":"2023","unstructured":"Kherraz T, Benbachir M, Lakrib M, Samei ME, Kaabar MKA, Bhanotar SA (2023) Existence and uniqueness results for fractional boundary value problems with multiple orders of fractional derivatives and integrals. Chaos Solitons Fractals 166(1):113007. https:\/\/doi.org\/10.1016\/j.chaos.2022.113007","journal-title":"Chaos Solitons Fractals"},{"key":"2681_CR21","volume-title":"Theory and applications of fractional differential equations. North-Holland mathematics studies","author":"AA Kilbas","year":"2006","unstructured":"Kilbas AA, Srivastava HM, Trujillo JJ (2006) Theory and applications of fractional differential equations. North-Holland mathematics studies. Elsevier, Amsterdam"},{"issue":"2","key":"2681_CR22","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1007\/s40314-022-01800-x","volume":"38","author":"KD Kucche","year":"2019","unstructured":"Kucche KD, Mali AD, Sousa JVC (2019) On the nonlinear $$\\psi $$-Hilfer fractional differential equations. Comput Appl Math 38(2):73. https:\/\/doi.org\/10.1007\/s40314-022-01800-x","journal-title":"Comput Appl Math"},{"issue":"15","key":"2681_CR23","doi-asserted-by":"publisher","first-page":"8608","DOI":"10.1002\/mma.6521","volume":"43","author":"AD Mali","year":"2020","unstructured":"Mali AD, Kucche KD (2020) Nonlocal boundary value problem for generalized Hilfer implicit fractional differential equations. Math Methods Appl Sci 43(15):8608\u20138631. https:\/\/doi.org\/10.1002\/mma.6521","journal-title":"Math Methods Appl Sci"},{"key":"2681_CR24","doi-asserted-by":"publisher","unstructured":"Patle PR, Gabeleh M, Rako\u010devi\u0107 V, Samei ME (2023) New best proximity point (pair) theorems via MNC and application to the existence of optimum solutions for a system of $$\\psi $$-Hilfer fractional differential equations. Revista de la Real Academia de Ciencias Exactas, F\u00edsicas y Naturales. Serie A. Matem\u00e1ticas 117:124. https:\/\/doi.org\/10.1007\/s13398-023-01451-5","DOI":"10.1007\/s13398-023-01451-5"},{"issue":"6","key":"2681_CR25","doi-asserted-by":"publisher","first-page":"2","DOI":"10.4172\/2090-0902.1000146","volume":"6","author":"ECFA Rosa","year":"2015","unstructured":"Rosa ECFA, de Oliveira EC (2015) Relaxation equations: fractional models. J Phys Math 6(6):2. https:\/\/doi.org\/10.4172\/2090-0902.1000146","journal-title":"J Phys Math"},{"key":"2681_CR26","volume-title":"Fractional integrals and derivatives: theory and applications","author":"SG Samko","year":"1993","unstructured":"Samko SG, Kilbas AA, Marichev OI (1993) Fractional integrals and derivatives: theory and applications. Gordon and Breach Science Publishers, Philadelphia"},{"key":"2681_CR27","doi-asserted-by":"publisher","first-page":"294","DOI":"10.1186\/s13662-021-03450-5","volume":"2021","author":"W Shatanawi","year":"2021","unstructured":"Shatanawi W, Boutiara A, Abdo MS, Jeelani MB, Abodayeh K (2021) Nonlocal and multiple-point fractional boundary value problem in the frame of a generalized Hilfer derivative. Adv Differ Equ 2021:294. https:\/\/doi.org\/10.1186\/s13662-021-03450-5","journal-title":"Adv Differ Equ"},{"issue":"15","key":"2681_CR28","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1016\/j.aml.2018.08.013","volume":"88","author":"JVC Sousa","year":"2019","unstructured":"Sousa JVC, Kucche KD, Oliveira EC (2019) Stability of $$\\psi $$-Hilfer impulsive fractional differential equations. Appl Math Lett 88(15):73\u201380. https:\/\/doi.org\/10.1016\/j.aml.2018.08.013","journal-title":"Appl Math Lett"},{"key":"2681_CR29","doi-asserted-by":"publisher","first-page":"72","DOI":"10.1016\/j.cnsns.2018.01.005","volume":"60","author":"JVDC Sousa","year":"2018","unstructured":"Sousa JVDC, Oliveira ECD (2018) On the $$\\psi $$-Hilfer fractional derivative. Commun Nonlinear Sci Numer Simul 60:72\u201391. https:\/\/doi.org\/10.1016\/j.cnsns.2018.01.005","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"2681_CR30","doi-asserted-by":"publisher","first-page":"196","DOI":"10.1007\/s11784-018-0587-5","volume":"20","author":"JVC Sousa","year":"2018","unstructured":"Sousa JVC, Oliveira EC (2018) On the Ulam\u2013Hyers\u2013Rassias stability for nonlinear fractional differential equations using the $$\\psi $$-Hilfer operator. J Fixed Point Theory Appl 20:196. https:\/\/doi.org\/10.1007\/s11784-018-0587-5","journal-title":"J Fixed Point Theory Appl"},{"issue":"4","key":"2681_CR31","doi-asserted-by":"publisher","first-page":"692","DOI":"10.3934\/Math.2017.4.692","volume":"2","author":"JVdC Sousa","year":"2017","unstructured":"Sousa JVdC, de Oliveira EC, Magna LA (2017) Fractional calculus and the ESR test. AIMS Math 2(4):692\u2013705. https:\/\/doi.org\/10.3934\/Math.2017.4.692","journal-title":"AIMS Math"},{"issue":"1\/2","key":"2681_CR32","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1016\/j.ajmsc.2019.03.001","volume":"26","author":"ST Thabet","year":"2020","unstructured":"Thabet ST, Ahmad B, Agarwal RP (2020) On abstract Hilfer fractional integrodifferential equations with boundary conditions. Arab J Math Sci 26(1\/2):107\u2013125. https:\/\/doi.org\/10.1016\/j.ajmsc.2019.03.001","journal-title":"Arab J Math Sci"},{"issue":"8","key":"2681_CR33","doi-asserted-by":"publisher","first-page":"607","DOI":"10.3390\/fractalfract7080607","volume":"7","author":"STM Thabet","year":"2023","unstructured":"Thabet STM, Vivas-Cortez M, Kedim I, Samei ME, Ayari MI (2023) Solvability of $$\\varrho $$-Hilfer fractional snap dynamic system on unbounded domains. Fractals Fract 7(8):607. https:\/\/doi.org\/10.3390\/fractalfract7080607","journal-title":"Fractals Fract"},{"issue":"6","key":"2681_CR34","doi-asserted-by":"publisher","first-page":"12576","DOI":"10.3934\/math.2023632","volume":"8","author":"STM Thabet","year":"2023","unstructured":"Thabet STM, Matar MM, Salman MA, Samei ME, Vivas-Cortez M (2023) On coupled snap system with integral boundary conditions in the $$\\mathbb{G} $$-Caputo sense. AIMS Math 8(6):12576\u201312605. https:\/\/doi.org\/10.3934\/math.2023632","journal-title":"AIMS Math"},{"key":"2681_CR35","doi-asserted-by":"publisher","first-page":"850","DOI":"10.1016\/j.amc.2015.05.144","volume":"266","author":"J Wang","year":"2015","unstructured":"Wang J, Zhang Y (2015) Nonlocal initial value problems for differential equations with Hilfer fractional derivative. Appl Math Comput 266:850\u2013859. https:\/\/doi.org\/10.1016\/j.amc.2015.05.144","journal-title":"Appl Math Comput"},{"key":"2681_CR36","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s13662-014-0331-4","volume":"161","author":"A Yang","year":"2015","unstructured":"Yang A, Henderson J, Nelms C Jr (2015) Extremal points for a higher-order fractional boundary-value problem. Electron J Differ Equ 161:1\u201312","journal-title":"Electron J Differ Equ"},{"key":"2681_CR37","doi-asserted-by":"publisher","DOI":"10.1142\/9069","volume-title":"Basic theory of fractional differential equations","author":"Y Zhou","year":"2014","unstructured":"Zhou Y (2014) Basic theory of fractional differential equations. World Scientific, Singapore"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-024-02681-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-024-02681-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-024-02681-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,8]],"date-time":"2024-04-08T05:02:31Z","timestamp":1712552551000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-024-02681-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4]]},"references-count":37,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,4]]}},"alternative-id":["2681"],"URL":"https:\/\/doi.org\/10.1007\/s40314-024-02681-y","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,4]]},"assertion":[{"value":"5 September 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 November 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 March 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 April 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"155"}}