Topology of Locally and Non-Locally Generalized Derivatives
This article investigates the continuity of derivatives of real-valued functions from a topological perspective. This is achieved by the characterization of their sets of discontinuity. The same principle is applied to Gateaux derivatives and gradients in Euclidean spaces. This article also introduc...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-01-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/1/53 |
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| _version_ | 1832588454003736576 |
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| author | Dimiter Prodanov |
| author_facet | Dimiter Prodanov |
| author_sort | Dimiter Prodanov |
| collection | DOAJ |
| description | This article investigates the continuity of derivatives of real-valued functions from a topological perspective. This is achieved by the characterization of their sets of discontinuity. The same principle is applied to Gateaux derivatives and gradients in Euclidean spaces. This article also introduces a generalization of the derivatives from the perspective of the modulus of continuity and characterizes their sets of discontinuities. There is a need for such generalizations when dealing with physical phenomena, such as fractures, shock waves, turbulence, Brownian motion, etc. |
| format | Article |
| id | doaj-art-ee042ef3cf434c24be85474ee04dd772 |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-ee042ef3cf434c24be85474ee04dd7722025-01-24T13:33:30ZengMDPI AGFractal and Fractional2504-31102025-01-01915310.3390/fractalfract9010053Topology of Locally and Non-Locally Generalized DerivativesDimiter Prodanov0Laboratory of Neurotechnology (PAML-LN), Institute for Information and Communication Technologies (IICT), Bulgarian Academy of Sciences, 1113 Sofia, BulgariaThis article investigates the continuity of derivatives of real-valued functions from a topological perspective. This is achieved by the characterization of their sets of discontinuity. The same principle is applied to Gateaux derivatives and gradients in Euclidean spaces. This article also introduces a generalization of the derivatives from the perspective of the modulus of continuity and characterizes their sets of discontinuities. There is a need for such generalizations when dealing with physical phenomena, such as fractures, shock waves, turbulence, Brownian motion, etc.https://www.mdpi.com/2504-3110/9/1/53singular functionsnon-differentiable functionsderivativescontinuityfractional derivatives and integrals |
| spellingShingle | Dimiter Prodanov Topology of Locally and Non-Locally Generalized Derivatives Fractal and Fractional singular functions non-differentiable functions derivatives continuity fractional derivatives and integrals |
| title | Topology of Locally and Non-Locally Generalized Derivatives |
| title_full | Topology of Locally and Non-Locally Generalized Derivatives |
| title_fullStr | Topology of Locally and Non-Locally Generalized Derivatives |
| title_full_unstemmed | Topology of Locally and Non-Locally Generalized Derivatives |
| title_short | Topology of Locally and Non-Locally Generalized Derivatives |
| title_sort | topology of locally and non locally generalized derivatives |
| topic | singular functions non-differentiable functions derivatives continuity fractional derivatives and integrals |
| url | https://www.mdpi.com/2504-3110/9/1/53 |
| work_keys_str_mv | AT dimiterprodanov topologyoflocallyandnonlocallygeneralizedderivatives |