{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,24]],"date-time":"2025-10-24T16:47:46Z","timestamp":1761324466082,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,8,10]],"date-time":"2022-08-10T00:00:00Z","timestamp":1660089600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science Foundation of Shandong Province","award":["ZR2018MA019"],"award-info":[{"award-number":["ZR2018MA019"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, by using the cosine family theory, measure of non-compactness, the M\u00f6nch fixed point theorem and the method of estimate step by step, we establish the existence theorems of mild solutions for fractional impulsive integro-differential evolution equations of order 1&lt;\u03b2\u22642 with nonlocal conditions in Banach spaces under some weaker conditions. The results obtained herein generalizes and improves some known results. Finally, an example is presented for the demonstration of obtained results.<\/jats:p>","DOI":"10.3390\/sym14081655","type":"journal-article","created":{"date-parts":[[2022,8,11]],"date-time":"2022-08-11T23:05:49Z","timestamp":1660259149000},"page":"1655","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Mild Solutions for Fractional Impulsive Integro-Differential Evolution Equations with Nonlocal Conditions in Banach Spaces"],"prefix":"10.3390","volume":"14","author":[{"given":"Ye","family":"Li","sequence":"first","affiliation":[{"name":"Institute of Operations Research, Qufu Normal University, Jining 273165, China"},{"name":"School of Data and Computer Science, Shandong Women\u2019s University, Jining 250062, China"}]},{"given":"Biao","family":"Qu","sequence":"additional","affiliation":[{"name":"Institute of Operations Research, Qufu Normal University, Jining 273165, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,10]]},"reference":[{"unstructured":"Podlubny, I. (1999). Fractional Differential Equations, Academic Press.","key":"ref_1"},{"doi-asserted-by":"crossref","unstructured":"Das, S. (2011). Functional Fractional Calculus, Springer.","key":"ref_2","DOI":"10.1007\/978-3-642-20545-3"},{"doi-asserted-by":"crossref","unstructured":"Milici, C., Dr\u0103g \u0103nescu, G., and Machado, J.T. (2019). Introduction to Fractional Differential Equations, Springer.","key":"ref_3","DOI":"10.1007\/978-3-030-00895-6"},{"unstructured":"Kilbas, A.A., Srivastava, H.M., and Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations, Elsevier.","key":"ref_4"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/j.aml.2016.05.010","article-title":"Local and global existence of mild solutions for a class of nonlinear fractional reaction-diffusion equations with delay","volume":"61","author":"Zhu","year":"2016","journal-title":"Appl. Math. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1108","DOI":"10.1016\/j.camwa.2014.01.002","article-title":"On the initial value problem of fractional evolution equations with noncompact semigroup","volume":"67","author":"Chen","year":"2014","journal-title":"Comput. Math. Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1811","DOI":"10.1016\/j.camwa.2016.01.028","article-title":"Existence and uniqueness of global mild solutions for a class of nonlinear fractional reactiondiffusion equations with delay","volume":"78","author":"Zhu","year":"2019","journal-title":"Comput. Math. Appl."},{"key":"ref_8","first-page":"1334","article-title":"Existence of solutions for a class of Mixed Fractional Order Semilinear integro-differential equations","volume":"39","author":"Zhu","year":"2019","journal-title":"Acta Math. Sin."},{"key":"ref_9","first-page":"911","article-title":"On the nonlocal Cauchy problem for semilinear fractional order evolution equations","volume":"12","author":"Wang","year":"2014","journal-title":"Cent. Eur. J. Math."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"510","DOI":"10.1016\/j.jmaa.2012.02.057","article-title":"Existence of mild solutions for fractional integrodifferential equations of Sobolev type with nonlocal conditions","volume":"391","author":"Li","year":"2012","journal-title":"J. Math. Anal. Appl."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"591","DOI":"10.2478\/s13540-012-0041-0","article-title":"Existence results for semilinear fractional differential equations via Kuratowski measure of noncompactness","volume":"15","author":"Li","year":"2012","journal-title":"Fract. Calc. Appl. Anal."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1435","DOI":"10.1016\/j.aml.2011.03.026","article-title":"A note on the fractional Cauchy problems with nonlocal initial conditions","volume":"24","author":"Wang","year":"2011","journal-title":"Appl. Math. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"4465","DOI":"10.1016\/j.nonrwa.2010.05.029","article-title":"Nonlocal Cauchy problem for fractional evolution equations","volume":"11","author":"Zhou","year":"2010","journal-title":"Nonlinear Anal. Real World Appl."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1016\/j.cnsns.2016.05.021","article-title":"Local and global existence of mild solution to impulsive fractional semilinear integro-differential equation with noncompact semigroup","volume":"42","author":"Gou","year":"2017","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_15","first-page":"105","article-title":"Existence and uniqueness of the mild solutions fora class of fractional non-autonomous with impulses","volume":"39","author":"Zhu","year":"2019","journal-title":"Acta Math. Sin."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2100","DOI":"10.1016\/j.camwa.2012.04.006","article-title":"The existence and uniqueness of mild solutions for fractional differential equations with nonlocal conditions of order 1 < \u03b2 \u2264 2","volume":"64","author":"Shu","year":"2012","journal-title":"Comput. Math. Appl."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1338","DOI":"10.1515\/fca-2017-0071","article-title":"Local and global existence of mild solutions for a class of semilinear fractional integro-differential equations","volume":"20","author":"Zhu","year":"2017","journal-title":"Fract. Calc. Appl. Anal."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1007\/s11784-016-0281-4","article-title":"Decay mild solutions for two-term time fractional differential equations in Banach spaces","volume":"18","author":"Luong","year":"2016","journal-title":"J. Fixed Point Theory Appl."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00009-016-0813-6","article-title":"Controllability of second-order impulsive nonlocal Cauchy problem via measure of noncompactness","volume":"14","author":"Vijayakumar","year":"2017","journal-title":"Mediterr. J. Math."},{"key":"ref_20","first-page":"107","article-title":"Approximate controllability of semilinear evolution equations of fractional order with nonlocal and impulsive conditions via an approximating technique","volume":"275","author":"Ge","year":"2016","journal-title":"Appl. Math. Comput."},{"key":"ref_21","first-page":"227","article-title":"Partial-approximate control lability of nonlocal fractional evolution equations via approximating method","volume":"334","author":"Mahmudov","year":"2018","journal-title":"Appl. Math. Comput."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1186\/s13662-015-0399-5","article-title":"Approximate controllability and optimal controls of fractional dynamical systems of order 1 < q < 2 in Banach spaces","volume":"2015","author":"Qin","year":"2015","journal-title":"Adv. Differ. Equ."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1016\/j.cam.2013.06.015","article-title":"On the approximate controllability of fractional evolution equations with compact analytic semigroup","volume":"259","author":"Mahmudov","year":"2014","journal-title":"J. Comput. Appl. Math."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/S0034-4877(13)60020-8","article-title":"Controllability of nonlocal fractional differential systems of order \u03b1 \u2208(1,2] in Banach spaces","volume":"71","author":"Li","year":"2013","journal-title":"Rep. Math. Phys."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"293","DOI":"10.22436\/jmcs.017.02.11","article-title":"Controllability of abstract fractional differential evolution equations with nonlocal conditions","volume":"17","author":"Qin","year":"2017","journal-title":"J. Math. Comput. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"C1807","DOI":"10.1360\/SSM-2020-0197","article-title":"Existence and uniqueness of mild solutions for fractional impulsive integro-differential evolution equations of order 1 < \u03b2 \u2264 2 with nonlocal conditions","volume":"50","author":"Liu","year":"2020","journal-title":"Sci. Sin. Math."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1016\/S0362-546X(99)00116-9","article-title":"Iterative method for solutions and coupled quasi-solutions of nonlinear integro-differential equations of mixed type in Banach spaces","volume":"42","author":"Liu","year":"2000","journal-title":"Nonlinear Anal."},{"doi-asserted-by":"crossref","unstructured":"Lakshmikantham, V., Bainov, D.D., and Simeonov, P.S. (1989). Theory of Impulsive Differential Equations, World Scientific.","key":"ref_28","DOI":"10.1142\/0906"},{"doi-asserted-by":"crossref","unstructured":"Deimling, K. (1985). Nonlinear Functional Analysis, Spinger.","key":"ref_29","DOI":"10.1007\/978-3-662-00547-7"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/8\/1655\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:07:00Z","timestamp":1760141220000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/8\/1655"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,10]]},"references-count":29,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["sym14081655"],"URL":"https:\/\/doi.org\/10.3390\/sym14081655","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,8,10]]}}}