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Kumar S, Chauhan R, Abdel-Aty AH, Abdelwahab SF. A study on fractional tumour–immune–vitamins model for intervention of vitamins. RESULTS IN PHYSICS 2022. [DOI: 10.1016/j.rinp.2021.104963] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
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Arfan M, Alrabaiah H, Rahman MU, Sun YL, Hashim AS, Pansera BA, Ahmadian A, Salahshour S. Investigation of fractal-fractional order model of COVID-19 in Pakistan under Atangana-Baleanu Caputo (ABC) derivative. RESULTS IN PHYSICS 2021; 24:104046. [PMID: 33868907 PMCID: PMC8044634 DOI: 10.1016/j.rinp.2021.104046] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2021] [Revised: 03/01/2021] [Accepted: 03/03/2021] [Indexed: 05/20/2023]
Abstract
This manuscript addressing the dynamics of fractal-fractional type modified SEIR model under Atangana-Baleanu Caputo (ABC) derivative of fractional order y and fractal dimension p for the available data in Pakistan. The proposed model has been investigated for qualitative analysis by applying the theory of non-linear functional analysis along with fixed point theory. The fractional Adams-bashforth iterative techniques have been applied for the numerical solution of the said model. The Ulam-Hyers (UH) stability techniques have been derived for the stability of the considered model. The simulation of all compartments has been drawn against the available data of covid-19 in Pakistan. The whole study of this manuscript illustrates that control of the effective transmission rate is necessary for stoping the transmission of the outbreak. This means that everyone in the society must change their behavior towards self-protection by keeping most of the precautionary measures sufficient for controlling covid-19.
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Affiliation(s)
- Muhammad Arfan
- Department of Mathematics, University of Malakand, Chakdara Dir (L), KPK, Pakistan
| | - Hussam Alrabaiah
- Al Ain University, Al Ain, United Arab Emirates
- Mathematics Department, Tafila Technical University, Tafila, Jordan
| | - Mati Ur Rahman
- Department of Mathematics, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, PR China
| | - Yu-Liang Sun
- School of Science, Huzhou University, Huzhou 313000, PR China
| | - Ahmad Sobri Hashim
- Computer & Information Sciences Department, Universiti Teknologi PETRONAS, 32610 Seri Iskandar, Perak, Malaysia
| | - Bruno A Pansera
- Department of Law, Economics and Human Sciences & Decisions Lab, Mediterranea University of Reggio Calabria, Reggio Calabria 89125, Italy
| | - Ali Ahmadian
- Institute of IR 4.0, The National University of Malaysia, Bangi, 43600 UKM, Selangor, Malaysia
- School of Mathematical Sciences, College of Science and Technology Wenzhou-Kean University, Wenzhou, PR China
| | - Soheil Salahshour
- Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey
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Ahmad N, Ullah A, Ullah A, Ahmad S, Shah K, Ahmad I. On analysis of the fuzzy fractional order Volterra-Fredholm integro-differential equation. ALEXANDRIA ENGINEERING JOURNAL 2021; 60:1827-1838. [DOI: 10.1016/j.aej.2020.11.031] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
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