{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,16]],"date-time":"2026-02-16T17:30:51Z","timestamp":1771263051130,"version":"3.50.1"},"reference-count":20,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,11,22]],"date-time":"2021-11-22T00:00:00Z","timestamp":1637539200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007345","name":"King Mongkut's University of Technology North Bangkok","doi-asserted-by":"publisher","award":["KMUTNB-63-KNOW-20"],"award-info":[{"award-number":["KMUTNB-63-KNOW-20"]}],"id":[{"id":"10.13039\/501100007345","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this manuscript, we establish the mild solutions for Hilfer fractional derivative integro-differential equations involving jump conditions and almost sectorial operator. For this purpose, we identify the suitable definition of a mild solution for this evolution equations and obtain the existence results. In addition, an application is also considered.<\/jats:p>","DOI":"10.3390\/axioms10040313","type":"journal-article","created":{"date-parts":[[2021,11,23]],"date-time":"2021-11-23T02:55:17Z","timestamp":1637636117000},"page":"313","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Mild Solutions for Impulsive Integro-Differential Equations Involving Hilfer Fractional Derivative with almost Sectorial Operators"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4138-7067","authenticated-orcid":false,"given":"Kulandhaivel","family":"Karthikeyan","sequence":"first","affiliation":[{"name":"Department of Mathematics & Centre for Research and Development, KPR Institute of Engineering and Technology, Coimbatore 641 407, India"}]},{"given":"Panjaiyan","family":"Karthikeyan","sequence":"additional","affiliation":[{"name":"PG and Research Department of Mathematics, Sri Vasavi College, Erode 638 136, India"}]},{"given":"Nichaphat","family":"Patanarapeelert","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8455-1402","authenticated-orcid":false,"given":"Thanin","family":"Sitthiwirattham","sequence":"additional","affiliation":[{"name":"Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,22]]},"reference":[{"key":"ref_1","first-page":"56","article-title":"Integral boundary value problems for fractional impulsive integro differential equations in Banach spaces","volume":"5","author":"Anguraj","year":"2014","journal-title":"Int. J. Anal. Appl."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Benchohra, M., Henderson, J., and Ntouyas, S.K. (2006). Impulsive Differential Equations and Inclusions, Hindawi Publishing Corporation.","DOI":"10.1155\/9789775945501"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1186\/s13662-018-1679-7","article-title":"Impulsive Hilfer fractional derivative differential equations","volume":"2018","author":"Ahmed","year":"2018","journal-title":"Adv. Differ. Equ."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1438","DOI":"10.1002\/mma.6843","article-title":"Results on the existence of Hilfer fractional neutral evolution equations with infinite delay via measures of noncompactness","volume":"44","author":"Kavitha","year":"2021","journal-title":"Math. Methods Appl. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2891","DOI":"10.1016\/j.aej.2020.01.055","article-title":"New results on nonlocal functional integro-differential equations via Hilfer fractional derivative","volume":"59","author":"Subashini","year":"2020","journal-title":"Alex. Eng. J."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1080\/02331930500530401","article-title":"Nonlinear impulsive integro-differential equations of mixed type and optimal controls","volume":"55","author":"Wei","year":"2006","journal-title":"Optimization"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Jaiswal, A., and Bahuguna, D. (2020). Hilfer Fractional Differential Equations with Almost Sectorial Operators. Differ. Equ. Dyn. Syst.","DOI":"10.1007\/s12591-020-00514-y"},{"key":"ref_8","unstructured":"Abdo, S.M., Panchal, S.K., and Bhairat, S.P. (2019). Existence of solution for Hilfer fractional differential equations with boundary value conditions. arXiv."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Wongcharoen, A., Ntouyas, S.K., and Tariboon, J. (2020). Boundary value problems for Hilfer fractional differential inclusions with nonlocal integral boundary conditions. Mathematics, 8.","DOI":"10.3390\/math8111905"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1007\/s00009-020-01512-8","article-title":"Constructive existence of solutions of multi-point boundary value problem for Hilfer fractional differential equation at Resonance","volume":"17","author":"Yong","year":"2020","journal-title":"Mediterr. J. Math."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"110944","DOI":"10.1016\/j.chaos.2021.110944","article-title":"A note on the mild solutions of Hilfer impulsive fractional differential equations","volume":"147","author":"Sousa","year":"2021","journal-title":"Chaos Solitons Fractals"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1007\/s43034-020-00095-5","article-title":"Existence of mild solutions to Hilfer fractional evolution equations in Banach space","volume":"12","author":"Sousa","year":"2021","journal-title":"Ann. Funct. Anal."},{"key":"ref_13","first-page":"592","article-title":"Existence and uniqueness of mild and strong solutions for fractional evolution equation","volume":"10","author":"Sousa","year":"2021","journal-title":"Palest. J. Math."},{"key":"ref_14","first-page":"145","article-title":"Fractional Cauchy problems with almost sectorial operators","volume":"257","author":"Zhang","year":"2015","journal-title":"Appl. Math. Comput."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Zhou, Y. (2014). Basic Theory of Fractional Differential Equations, World Scientific.","DOI":"10.1142\/9069"},{"key":"ref_16","first-page":"344","article-title":"Existence of mild solution for evolution equation with Hilfer fractional derivative derivative","volume":"257","author":"Gu","year":"2015","journal-title":"Appl. Math. Comput."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Lakshmikantham, V., Bainov, D.D., and Simeonov, P.S. (1989). Theory of Impulsive Differential Equations, Worlds Scientifc.","DOI":"10.1142\/0906"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"985","DOI":"10.1016\/0362-546X(80)90010-3","article-title":"Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces","volume":"4","author":"Monch","year":"1980","journal-title":"Nonlinear Anal. Theory Methods Appl."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/BF02783044","article-title":"Multivalued perturbation of m-accretive differential inclusions","volume":"108","author":"Bothe","year":"1998","journal-title":"Isr. J. Math."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Pazy, A. (1983). Semigroup of Linear Operators and Applications to Partial Differential Equations, Springer. Applied Mathematical Sciences.","DOI":"10.1007\/978-1-4612-5561-1"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/10\/4\/313\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:33:53Z","timestamp":1760168033000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/10\/4\/313"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,22]]},"references-count":20,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["axioms10040313"],"URL":"https:\/\/doi.org\/10.3390\/axioms10040313","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,22]]}}}