{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T00:00:05Z","timestamp":1773792005438,"version":"3.50.1"},"reference-count":36,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,4,25]],"date-time":"2020-04-25T00:00:00Z","timestamp":1587772800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This article deals with the solutions of the existence and uniqueness for a new class of boundary value problems (BVPs) involving nonlinear fractional differential equations (FDEs), inclusions, and boundary conditions involving the generalized fractional integral. The nonlinearity relies on the unknown function and its fractional derivatives in the lower order. We use fixed-point theorems with single-valued and multi-valued maps to obtain the desired results, through the support of illustrations, the main results are well explained. We also address some variants of the problem.<\/jats:p>","DOI":"10.3390\/axioms9020044","type":"journal-article","created":{"date-parts":[[2020,4,27]],"date-time":"2020-04-27T04:15:29Z","timestamp":1587960929000},"page":"44","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Existence of Solutions for Nonlinear Fractional Differential Equations and Inclusions Depending on Lower-Order Fractional Derivatives"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5281-0935","authenticated-orcid":false,"given":"Subramanian","family":"Muthaiah","sequence":"first","affiliation":[{"name":"Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore 641020, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0286-7244","authenticated-orcid":false,"given":"Dumitru","family":"Baleanu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Cankaya University, Balgat 06530, Ankara, Turkey"},{"name":"Institute of Space Science, 077125 Magurele-Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,25]]},"reference":[{"key":"ref_1","first-page":"445","article-title":"Analysis of fractional boundary value problem with non-local integral strip boundary conditions","volume":"26","author":"Subramanian","year":"2019","journal-title":"Nonlinear Stud."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Subramanian, M., Kumar, A.R.V., and Gopal, T.N. 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