{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T15:27:34Z","timestamp":1768318054505,"version":"3.49.0"},"reference-count":37,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,1,21]],"date-time":"2022-01-21T00:00:00Z","timestamp":1642723200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This research paper is dedicated to an investigation of an evolution problem under a new operator (g-Atangana\u2013Baleanu\u2013Caputo type fractional derivative)(for short, g-ABC). For the proposed problem, we construct sufficient conditions for some properties of the solution like existence, uniqueness and stability analysis. Existence and uniqueness results are proved based on some fixed point theorems such that Banach and Krasnoselskii. Furthermore, through mathematical analysis techniques, we analyze different types of stability results. The symmetric properties aid in identifying the best strategy for getting the correct solution of fractional differential equations. An illustrative example is discussed for the control problem.<\/jats:p>","DOI":"10.3390\/sym14020207","type":"journal-article","created":{"date-parts":[[2022,1,23]],"date-time":"2022-01-23T20:36:27Z","timestamp":1642970187000},"page":"207","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["A Qualitative Study on Second-Order Nonlinear Fractional Differential Evolution Equations with Generalized ABC Operator"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5719-086X","authenticated-orcid":false,"given":"Mohammed","family":"Almalahi","sequence":"first","affiliation":[{"name":"Department of Mathematics, Hajjah University, Hajjah 967, Yemen"},{"name":"Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad 431004, India"}]},{"given":"Amani","family":"Ibrahim","sequence":"additional","affiliation":[{"name":"Department of Statistics and Informatics Techniques, Technical College of Management-Mosul, Northern Technical University, Kirkuk 36001, Iraq"}]},{"given":"Alanoud","family":"Almutairi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Hafr Al Batin, P.O. Box 1803, Hafar Al Batin 31991, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7251-9608","authenticated-orcid":false,"given":"Omar","family":"Bazighifan","sequence":"additional","affiliation":[{"name":"Section of Mathematics, International Telematic University Uninettuno, CorsoVittorio Emanuele II, 39, 00186 Roma, Italy"},{"name":"Department of Mathematics, Faculty of Science, Hadhramout University, Mukalla 50512, Yemen"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4316-5895","authenticated-orcid":false,"given":"Tariq","family":"Aljaaidi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad 431004, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0387-921X","authenticated-orcid":false,"given":"Jan","family":"Awrejcewicz","sequence":"additional","affiliation":[{"name":"Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1\/15 Stefanowski St., 90-924 Lodz, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,21]]},"reference":[{"key":"ref_1","unstructured":"Podlubny, I. 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