{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T21:08:15Z","timestamp":1778188095090,"version":"3.51.4"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2025,7,4]],"date-time":"2025-07-04T00:00:00Z","timestamp":1751587200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,7,4]],"date-time":"2025-07-04T00:00:00Z","timestamp":1751587200000},"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":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2025,10]]},"DOI":"10.1007\/s12190-025-02579-w","type":"journal-article","created":{"date-parts":[[2025,7,4]],"date-time":"2025-07-04T10:40:07Z","timestamp":1751625607000},"page":"7521-7541","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Stability and solutions of adjoint nonlinear impulsive neutral mixed integral equations in dynamic systems"],"prefix":"10.1007","volume":"71","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-0139-6375","authenticated-orcid":false,"given":"C.","family":"Anusha","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0214-1280","authenticated-orcid":false,"given":"C.","family":"Ravichandran","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0009-7227-7379","authenticated-orcid":false,"given":"Fahad","family":"Aljuaydi","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5769-4320","authenticated-orcid":false,"given":"Kottakkaran Sooppy","family":"Nisar","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6146-5544","authenticated-orcid":false,"given":"Dimplekumar","family":"Chalishajar","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,7,4]]},"reference":[{"key":"2579_CR1","doi-asserted-by":"crossref","unstructured":"Bohner, M., Peterson, A.: Advances in dynamic equations on time scales.. Birkh\u00e4user, Boston, Mass, USA (2003)","DOI":"10.1007\/978-0-8176-8230-9"},{"key":"2579_CR2","doi-asserted-by":"crossref","unstructured":"Streipert, S.: Dynamic Equations on Time Scales. Nonlinear Syst. - Recent Developments Adv. Intech. (2023)","DOI":"10.5772\/intechopen.104691"},{"key":"2579_CR3","doi-asserted-by":"publisher","first-page":"897","DOI":"10.1007\/s12652-021-03343-1","volume":"14","author":"Z. Tian","year":"2023","unstructured":"Tian, Z.: Analysis and research on chaotic dynamics behaviour of wind power time series at different time scales. J. Ambient. Intell. Humaniz. Comput. 14, 897\u2013921 (2023)","journal-title":"J. Ambient. Intell. Humaniz. Comput."},{"key":"2579_CR4","first-page":"410","volume":"21","author":"S. Tikare","year":"2021","unstructured":"Tikare, S.: Nonlocal initial value problems for first order dynamic equations on time scale. Appl. Math. E-Notes 21, 410\u2013420 (2021)","journal-title":"Appl. Math. E-Notes"},{"key":"2579_CR5","volume-title":"Dynamic Equations on Time Scales and Applications.","year":"2024","unstructured":"Agarwal, R.P., Hazarika, B., Tikare, S. (eds.) Dynamic Equations on Time Scales and Applications.. CRC Press, Boca Raton (2024)"},{"issue":"3","key":"2579_CR6","doi-asserted-by":"publisher","first-page":"489","DOI":"10.18576\/pfda\/100313","volume":"10","author":"K.S. Nisar","year":"2024","unstructured":"Nisar, K.S., Farman, M., Abdel-Aty, M., Ravichandran, C.: A review of fractional-order models for plant epidemiology. Prog. Fract. Differ. Appl. 10(3), 489\u2013521 (2024)","journal-title":"Prog. Fract. Differ. Appl."},{"key":"2579_CR7","doi-asserted-by":"crossref","unstructured":"Ravichandran, C., Logeswari, K., Khan, A., Abdeljawad, T., G\u00f3mez-Aguilar, J.F.: An epidemiological model for computer virus with Atangana-Baleanu fractional derivative. Results Phys. 51, 106601 (2023)","DOI":"10.1016\/j.rinp.2023.106601"},{"issue":"7","key":"2579_CR8","doi-asserted-by":"publisher","first-page":"12091","DOI":"10.3934\/math.2022672","volume":"7","author":"C. Maji","year":"2022","unstructured":"Maji, C., Al Basir, F., Mukherjee, D., Nisar, K.S., Ravichandran, C.: COVID-19 propagation and the usefulness of awareness-based control measures: A mathematical model with delay. AIMS. Math. 7(7), 12091\u201312105 (2022)","journal-title":"AIMS. Math."},{"key":"2579_CR9","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1016\/j.aej.2024.03.059","volume":"95","author":"K.S. Nisar","year":"2024","unstructured":"Nisar, K.S., Farman, M., Abdel-Aty, M., Ravichandran, C.: A review of fractional order epidemic models for life sciences problems: Past, present and future. Alex. Eng. J. 95, 283\u2013305 (2024)","journal-title":"Alex. Eng. J."},{"key":"2579_CR10","doi-asserted-by":"publisher","first-page":"107414","DOI":"10.1016\/j.cnsns.2023.107414","volume":"125","author":"A. Khatoon","year":"2023","unstructured":"Khatoon, A., Raheem, A., Afreen, A.: Approximate solutions for neutral stochastic fractional differential equations. Commun. Nonlinear Sci. Numer. Simul. 125, 107414 (2023)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"issue":"1","key":"2579_CR11","doi-asserted-by":"publisher","first-page":"1911","DOI":"10.3934\/math.2024094","volume":"9","author":"K.S. Nisar","year":"2023","unstructured":"Nisar, K.S., Anusha, C., Ravichandran, C.: A non-linear fractional neutral dynamic equations: existence and stability results on time scales. AIMS. Math. 9(1), 1911\u20131925 (2023)","journal-title":"AIMS. Math."},{"key":"2579_CR12","doi-asserted-by":"publisher","first-page":"667","DOI":"10.1007\/s10959-013-0520-1","volume":"28","author":"H.M. Ahmed","year":"2015","unstructured":"Ahmed, H.M.: Semilinear neutral fractional stochastic integro-differential equations with nonlocal conditions. J. Theor. Probab. 28, 667\u2013680 (2015)","journal-title":"J. Theor. Probab."},{"issue":"1","key":"2579_CR13","doi-asserted-by":"publisher","first-page":"e22652","DOI":"10.1002\/num.22652","volume":"40","author":"K. Logeswari","year":"2024","unstructured":"Logeswari, K., Ravichandran, C., Nisar, K.S.: Mathematical model for spreading of COVID-19 virus with the Mittag-Leffler kernel. Numer. Methods Partial Differ. Equ. 40(1), e22652 (2024)","journal-title":"Numer. Methods Partial Differ. Equ."},{"key":"2579_CR14","doi-asserted-by":"crossref","unstructured":"Chadha, A., Pandey, D.N.: Existence and approximation of solution to neutral fractional differential equation with nonlocal conditions. Comput. Math. Appl. 69(9), 893\u2013908 (2015)","DOI":"10.1016\/j.camwa.2015.02.003"},{"issue":"3","key":"2579_CR15","doi-asserted-by":"publisher","first-page":"5934","DOI":"10.3934\/math.2023299","volume":"8","author":"A. Morsy","year":"2022","unstructured":"Morsy, A., Nisar, K.S., Ravichandran, C., Anusha, C.: Sequential fractional order neutral functional integro differential equations on time scales with Caputo fractional operator over Banach spaces. AIMS. Math. 8(3), 5934\u20135949 (2022)","journal-title":"AIMS. Math."},{"key":"2579_CR16","doi-asserted-by":"crossref","unstructured":"Tripathy, A.K., Santra, S.S.: Necessary and sufficient conditions for oscillations to a second-order neutral differential equations with impulses. Kragujevac J. Math. 47(1), 81\u201393 (2023)","DOI":"10.46793\/KgJMat2301.081T"},{"key":"2579_CR17","doi-asserted-by":"crossref","unstructured":"Hamsavarthini, G., Ravichandran, C., Aljuaydi, F., Nisar, K.S.: A fractional-order framework for investigating groundwater depletion under environmental and human pressures. J. Appl. Math. Comput. 1\u20137 (2025)","DOI":"10.1007\/s12190-025-02514-z"},{"issue":"2","key":"2579_CR18","doi-asserted-by":"publisher","first-page":"249","DOI":"10.22436\/jmcs.039.02.05","volume":"39","author":"K.S. Nisar","year":"2025","unstructured":"Nisar, K.S., Hamsavarthini, G., Ravichandran, C., Kumaran, S.U.: Analyzing predator-prey dynamics in the context of global warming using fractional integro differential equations. J. Math. Comput. Sci. 39(2), 249\u2013262 (2025)","journal-title":"J. Math. Comput. Sci."},{"key":"2579_CR19","unstructured":"Knapik, R.: Impulsive differential equations with non local conditions. Morehead Electron. J. Appl. Math. 3 (2003)"},{"key":"2579_CR20","doi-asserted-by":"crossref","unstructured":"Shah, K., Abdalla, B., Abdeljawad, T., Gul, R.: Analysis of multipoint impulsive problem of fractional-order differential equations. Bound. Value. Probl. 1 (2023 (2023)","DOI":"10.1186\/s13661-022-01688-w"},{"issue":"2","key":"2579_CR21","doi-asserted-by":"publisher","first-page":"639","DOI":"10.3934\/dcdsb.2021059","volume":"27","author":"M. Bohner","year":"2022","unstructured":"Bohner, M., Tunc, O.: Qualitative analysis of integro-differential equations with variable retardation. Discrete Contin. Dyn. Syst. Ser. B 27(2), 639\u2013657 (2022)","journal-title":"Discrete Contin. Dyn. Syst. Ser. B"},{"key":"2579_CR22","doi-asserted-by":"crossref","unstructured":"Bohner, M., Tunc, O., Korkmaz, E.: On the fundamental qualitative properties of integro-delay differential equations. Commun. Nonlinear Sci. Numer. Simul. 125, 1\u201312 (2023)","DOI":"10.1016\/j.cnsns.2023.107320"},{"issue":"2","key":"2579_CR23","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1016\/j.cam.2004.07.026","volume":"176","author":"J.J. Dacunha","year":"2005","unstructured":"Dacunha, J.J.: Stability for time varying linear dynamic systems on time scales. J. Comput. Appl. Math. 176(2), 381\u2013410 (2005)","journal-title":"J. Comput. Appl. Math."},{"key":"2579_CR24","doi-asserted-by":"crossref","unstructured":"Tunc, O.: On the behaviors of solutions of systems of non-linear differential equations with multiple constant delays. Rev. R. Acad. Cienc. Exactas F\u00eds. Nat. Ser. A Mat. 115(164), 1\u201322 (2021)","DOI":"10.1007\/s13398-021-01104-5"},{"key":"2579_CR25","unstructured":"Ulam, S.M.: A Collection of the Mathematical Problems.. Interscience Publishers, New York-London (1960)"},{"key":"2579_CR26","volume-title":"Problem in Modern Mathematics.","author":"S.M. Ulam","year":"1964","unstructured":"Ulam, S.M.: Problem in Modern Mathematics., Science Editions. J. Wiley and Sons, Inc, New York (1964)","edition":"Science Edition"},{"issue":"4","key":"2579_CR27","doi-asserted-by":"publisher","first-page":"222","DOI":"10.1073\/pnas.27.4.222","volume":"27","author":"D.H. Hyers","year":"1941","unstructured":"Hyers, D.H.: On the stability of the linear functional equation. Proc. Natl. Acad. Sci. USA. 27(4), 222\u2013224 (1941)","journal-title":"Proc. Natl. Acad. Sci. USA."},{"issue":"2","key":"2579_CR28","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1090\/S0002-9939-1978-0507327-1","volume":"72","author":"T.M. Rassias","year":"1978","unstructured":"Rassias, T.M.: On the stability of linear mappings in Banach spaces. Proc. Amer. Math. Soc. 72(2), 297\u2013300 (1978)","journal-title":"Proc. Amer. Math. Soc."},{"key":"2579_CR29","volume-title":"Springer Optim. Its Appl.","author":"S.M. Jung","year":"2011","unstructured":"Jung, S.M.: Hyers-Ulam-Rassias stability of functional equations in nonlinear analysis. Springer Optim. Its Appl., vol. 48. Springer, New York (2011)"},{"issue":"2","key":"2579_CR30","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1080\/16583655.2018.1451117","volume":"12","author":"C. Tunc","year":"2018","unstructured":"Tunc, C., Tunc, O.: On behaviours of functional Volterra integro-differential equations with multiple time lags. J. Taibah Univ. Sci. 12(2), 173\u2013179 (2018)","journal-title":"J. Taibah Univ. Sci."},{"key":"2579_CR31","doi-asserted-by":"crossref","unstructured":"Shah, S.O., Rizwan, R., Rehman, S., Xia, Y.: Stability and controllability analysis of non-linear Volterra Fredholm Hammerstein impulsive integro-dynamic systems with delay on time scale. Alex. Eng. J. 87, 240\u2013276 (2024)","DOI":"10.1016\/j.aej.2023.12.024"},{"issue":"3-4","key":"2579_CR32","first-page":"241","volume":"11","author":"M. Bohner","year":"2021","unstructured":"Bohner, M., Tikare, S., Santos, I.L.D.D.: First-order nonlinear dynamic initial value problems. Int. J. Dyn. Syst. Differ. Equ. 11(3-4), 241\u2013254 (2021)","journal-title":"Int. J. Dyn. Syst. Differ. Equ."},{"issue":"106","key":"2579_CR33","first-page":"1","volume":"21","author":"M. Bohner","year":"2022","unstructured":"Bohner, M., Scindia, P.S., Tikare, S.: Qualitative results for nonlinear integro-dynamic equations via integral inequalities. Qual. Theory Dyn. Syst. 21(106), 1\u201329 (2022)","journal-title":"Qual. Theory Dyn. Syst."},{"key":"2579_CR34","doi-asserted-by":"crossref","unstructured":"Scindia, P., Tikare, S., El-Deeb, A.A.: Ulam stability of first-order nonlinear impulsive dynamic equations. Bound. Value. Probl. 86, 1\u201313 (2023 (2023)","DOI":"10.1186\/s13661-023-01752-z"},{"issue":"21","key":"2579_CR35","first-page":"1","volume":"11","author":"S.O. Shah","year":"2023","unstructured":"Shah, S.O., Tikare, S., Osman, M.: Ulam type stability results of nonlinear impulsive Volterra-Fredholm integro-dynamic adjoint equations on time scale. Math. 11(21), 1\u201312 (2023)","journal-title":"Math."},{"key":"2579_CR36","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1007\/s12346-024-01205-7","volume":"24","author":"S.O. Shah","year":"2025","unstructured":"Shah, S.O., Kumar, V., Tikare, S., Rizwan, R., Riaz, U.: Qualitative results of non-linear adjoint dynamic system with delays and impulses on arbitrary time domains. Qual. Theory Dyn. Syst. 24, 45 (2025)","journal-title":"Qual. Theory Dyn. Syst."},{"key":"2579_CR37","first-page":"202","volume":"359","author":"S.O. Shah","year":"2019","unstructured":"Shah, S.O., Zada, A.: Existence, uniqueness and stability of solution to mixed integral dynamic systems with instantaneous and noninstantaneous impulses on time scales. Appl. Math. Comput. 359, 202\u2013213 (2019)","journal-title":"Appl. Math. Comput."},{"issue":"1","key":"2579_CR38","doi-asserted-by":"publisher","first-page":"92","DOI":"10.3390\/fractalfract7010092","volume":"7","author":"H.A. Hammad","year":"2023","unstructured":"Hammad, H.A., Sen, M.D.: Stability and controllability study for mixed integral fractional delay dynamic systems endowed with impulsive effects on time scales. Fract. Fract. 7(1), 92 (2023)","journal-title":"Fract. Fract."},{"key":"2579_CR39","doi-asserted-by":"crossref","unstructured":"Bohner, M., Peterson, A.: Dynamic equations on time scales: an introduction with applications.. Birkh\u00e4user, Boston, Mass, USA (2001)","DOI":"10.1007\/978-1-4612-0201-1"}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-025-02579-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12190-025-02579-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-025-02579-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T15:10:56Z","timestamp":1759331456000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12190-025-02579-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,4]]},"references-count":39,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2025,10]]}},"alternative-id":["2579"],"URL":"https:\/\/doi.org\/10.1007\/s12190-025-02579-w","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"value":"1598-5865","type":"print"},{"value":"1865-2085","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,7,4]]},"assertion":[{"value":"27 April 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 June 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 June 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 July 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval and consent to participate:"}},{"value":"None.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}]}}