Theoretical investigation on fractal–fractional nonlinear ordinary differential equations

Abdon Atangana; Seda İğret Araz

Theoretical investigation on fractal–fractional nonlinear ordinary differential equations

dc.authorid	https://orcid.org/0000-0002-7698-0709
dc.contributor.author	Abdon Atangana
dc.contributor.author	Seda İğret Araz
dc.date.accessioned	2025-01-13T08:33:49Z
dc.date.available	2025-01-13T08:33:49Z
dc.date.issued	2025-08
dc.department	Fakülteler, Eğitim Fakültesi, Matematik ve Fen Bilimleri Eğitimi Bölümü
dc.description.abstract	In this study, we examine the existence and uniqueness conditions of the solutions of the nonlinear fractal-fractional differential equations. Particular emphasis is placed on four cases: exponential decay, power law, generalized Mittag-Leffler kernels and the Delta-Dirac function. Our first contribution is the formulation of some basic inequalities inspired from Gronwall inequality setting up a solid foundation for our analysis to follow. We subsequently carefully obtain the maximal and minimal solutions in each scenario, providing a complete picture of their structure. Finally we show convergence of four different successive approximation schemes, validating their applicability in the various contexts. This is an important finding that adds to the growing literature on the use of fractional calculus in complex dynamical systems.
dc.identifier.citation	Atangana, A., & Araz, S. İ. (2025). Theoretical investigation on fractal–fractional nonlinear ordinary differential equations. Nonlinear Analysis: Real World Applications, 84, 104296.
dc.identifier.doi	10.1016/j.nonrwa.2024.104296
dc.identifier.issn	https://10.1016/j.nonrwa.2024.104296
dc.identifier.issn	1468-1218
dc.identifier.scopus	2-s2.0-85214260423
dc.identifier.scopusquality	Q1
dc.identifier.uri	https://hdl.handle.net/20.500.12604/8437
dc.identifier.volume	84
dc.identifier.wosquality	Q1
dc.institutionauthor	İğret Araz, Seda
dc.institutionauthorid	https://orcid.org/0000-0002-7698-0709
dc.language.iso	en
dc.publisher	Elsevier BV
dc.relation.ispartof	Nonlinear Analysis: Real World Applications
dc.relation.publicationcategory	Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	Fractal–fractional differentiation and integration
dc.subject	Inequalities
dc.subject	Maximal and minimal solutions
dc.subject	Successive approximation
dc.title	Theoretical investigation on fractal–fractional nonlinear ordinary differential equations
dc.type	journal-article
oaire.citation.volume	84