Analysis of Cauchy problem with fractal-fractional differential operators

• Autorzy: Alharthi Nadiyah Hussain , Atangana Abdon , Alkahtani Badr S.

Identyfikatory

DOI

10.1515/dema-2022-0181

• Języki publikacji: EN

Abstrakty

EN

Cauchy problems with fractal-fractional differential operators with a power law, exponential decay, and the generalized Mittag-Leffler kernels are considered in this work. We start with deriving some important inequalities, and then by using the linear growth and Lipchitz conditions, we derive the conditions under which these equations admit unique solutions. A numerical scheme was suggested for each case to derive a numerical solution to the equation. Some examples of fractal-fractional differential equations were presented, and their exact solutions were obtained and compared with the used numerical scheme. A nonlinear case was considered and solved, and numerical solutions were presented graphically for different values of fractional orders and fractal dimensions.

Słowa kluczowe

EN

fractal-fractional; power law; exponential decay; Mittag-Leffler function; numerical scheme; inequalities

PL

prawo energetyczne; prawo rozpadu naturalnego; funkcja Mittag-Lefflera; schemat numeryczny; nierówności

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2023
• Tom: Vol. 56, nr 1
• Strony: art. no. 20220181
• Opis fizyczny: Bibliogr. 17 poz., wykr.

Twórcy

autor

Alharthi Nadiyah Hussain

• Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University College of Science, P.O. Box 90950, 11623, Riyadh, Saudi Arabia

autor

Atangana Abdon

• Institute for Groundwater Studies, Faculty of Natural and Agricultural Science, University of the Free State, 9300 Bloemfontein, South Africa
• Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

autor

Alkahtani Badr S.

• Department of Mathematics, College of Science, King Saud University, P.O. Box 1142, Riyadh 11989, Saudi Arabia

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).