New Coronavirus (2019-nCov) Mathematical Model Using Piecewise Hybrid Fractional Order Derivatives; Numerical Treatments
A new mathematical model of Coronavirus (2019-nCov) using piecewise hybrid fractional order derivatives is given in this paper. Moreover, in order to be consistent with the physical model problem, a new parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" dis...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-12-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/10/23/4579 |
| _version_ | 1797462753314603008 |
|---|---|
| author | Nasser H. Sweilam Seham M. AL-Mekhlafi Saleh M. Hassan Nehaya R. Alsenaideh Abdelaziz Elazab Radwan |
| author_facet | Nasser H. Sweilam Seham M. AL-Mekhlafi Saleh M. Hassan Nehaya R. Alsenaideh Abdelaziz Elazab Radwan |
| author_sort | Nasser H. Sweilam |
| collection | DOAJ |
| description | A new mathematical model of Coronavirus (2019-nCov) using piecewise hybrid fractional order derivatives is given in this paper. Moreover, in order to be consistent with the physical model problem, a new parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula> is presented. The boundedness, existence, and positivity of the solutions for the proposed model are discussed. Two improved numerical methods are presented in this paper. The Caputo proportional constant nonstandard modified Euler–Maruyama method is introduced to study the fractional stochastic model, and the Grünwald–Letnikov nonstandard finite difference method is presented to study the hybrid fractional order deterministic model. Comparative studies with real data from Spain and Wuhan are presented. |
| first_indexed | 2024-03-09T17:41:07Z |
| format | Article |
| id | doaj.art-eac29731d75f461fa26737c6abe62424 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T17:41:07Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-eac29731d75f461fa26737c6abe624242023-11-24T11:35:54ZengMDPI AGMathematics2227-73902022-12-011023457910.3390/math10234579New Coronavirus (2019-nCov) Mathematical Model Using Piecewise Hybrid Fractional Order Derivatives; Numerical TreatmentsNasser H. Sweilam0Seham M. AL-Mekhlafi1Saleh M. Hassan2Nehaya R. Alsenaideh3Abdelaziz Elazab Radwan4Mathematics Department, Faculty of Science, Cairo University, Giza 12613, EgyptMathematics Department, Faculty of Education, Sana’a University, Sana’a P.O. Box 1247, YemenMathematics Department, Faculty of Science, Ain Shams University, Cairo 11566, EgyptMathematics Department, Faculty of Science, Ain Shams University, Cairo 11566, EgyptMathematics Department, Faculty of Science, Ain Shams University, Cairo 11566, EgyptA new mathematical model of Coronavirus (2019-nCov) using piecewise hybrid fractional order derivatives is given in this paper. Moreover, in order to be consistent with the physical model problem, a new parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula> is presented. The boundedness, existence, and positivity of the solutions for the proposed model are discussed. Two improved numerical methods are presented in this paper. The Caputo proportional constant nonstandard modified Euler–Maruyama method is introduced to study the fractional stochastic model, and the Grünwald–Letnikov nonstandard finite difference method is presented to study the hybrid fractional order deterministic model. Comparative studies with real data from Spain and Wuhan are presented.https://www.mdpi.com/2227-7390/10/23/4579piecewise numerical methodshybrid fractional coronavirus (2019-nCov) mathematical modelsnonstandard fractional Euler–Maruyama techniquefractional stochastic–deterministic modelsGrünwald–Letnikov nonstandard finite difference method |
| spellingShingle | Nasser H. Sweilam Seham M. AL-Mekhlafi Saleh M. Hassan Nehaya R. Alsenaideh Abdelaziz Elazab Radwan New Coronavirus (2019-nCov) Mathematical Model Using Piecewise Hybrid Fractional Order Derivatives; Numerical Treatments Mathematics piecewise numerical methods hybrid fractional coronavirus (2019-nCov) mathematical models nonstandard fractional Euler–Maruyama technique fractional stochastic–deterministic models Grünwald–Letnikov nonstandard finite difference method |
| title | New Coronavirus (2019-nCov) Mathematical Model Using Piecewise Hybrid Fractional Order Derivatives; Numerical Treatments |
| title_full | New Coronavirus (2019-nCov) Mathematical Model Using Piecewise Hybrid Fractional Order Derivatives; Numerical Treatments |
| title_fullStr | New Coronavirus (2019-nCov) Mathematical Model Using Piecewise Hybrid Fractional Order Derivatives; Numerical Treatments |
| title_full_unstemmed | New Coronavirus (2019-nCov) Mathematical Model Using Piecewise Hybrid Fractional Order Derivatives; Numerical Treatments |
| title_short | New Coronavirus (2019-nCov) Mathematical Model Using Piecewise Hybrid Fractional Order Derivatives; Numerical Treatments |
| title_sort | new coronavirus 2019 ncov mathematical model using piecewise hybrid fractional order derivatives numerical treatments |
| topic | piecewise numerical methods hybrid fractional coronavirus (2019-nCov) mathematical models nonstandard fractional Euler–Maruyama technique fractional stochastic–deterministic models Grünwald–Letnikov nonstandard finite difference method |
| url | https://www.mdpi.com/2227-7390/10/23/4579 |
| work_keys_str_mv | AT nasserhsweilam newcoronavirus2019ncovmathematicalmodelusingpiecewisehybridfractionalorderderivativesnumericaltreatments AT sehammalmekhlafi newcoronavirus2019ncovmathematicalmodelusingpiecewisehybridfractionalorderderivativesnumericaltreatments AT salehmhassan newcoronavirus2019ncovmathematicalmodelusingpiecewisehybridfractionalorderderivativesnumericaltreatments AT nehayaralsenaideh newcoronavirus2019ncovmathematicalmodelusingpiecewisehybridfractionalorderderivativesnumericaltreatments AT abdelazizelazabradwan newcoronavirus2019ncovmathematicalmodelusingpiecewisehybridfractionalorderderivativesnumericaltreatments |