Analysis of Energy Sector Model with Laplace Transform under modified fractional operator: Mathematical Analysis

Muhammad Kamran; Aamir Shehzad

doi:10.48165/jmmfc.2024.1203

Authors

Muhammad Kamran Research Institute of Business Analytics and Supply Chain Management, Shenzhen University, China.
Aamir Shehzad Mathematics Research Center, Near East University, 99138 Nicosia, Cyprus, Turkey.

DOI:

https://doi.org/10.48165/jmmfc.2024.1203

Keywords:

Carbon dioxide emission, Mathematical Model, Fractional operators, Lipschitz criteria

Abstract

Population growth is driving up energy demand, and burning fossil fuels accounts for a sizable amount of global energy production. Since this adds to the rise in greenhouse gas emissions, lowering energy sector emissions is essential to achieving climate change goals. In this research, three hybrid fractional operators are used to investigate carbon emissions from the power sector. A hy brid fractional operator is used to modify differential equations throughout time and space in order to create a mathematical model that describes the human population, energy consumption, and at mospheric carbon dioxide concentration. Compartmental models offer a mathematical framework for comprehending systems and forecasting outcomes, which makes them essential fgor comprehending real-world events. The effectiveness of these novel operators is supported by a number of analyses, and the Lipschitz condition ensures unique results. The order of the fractional derivative has a major impact on the dynamical process that is used to construct the non-integer order model.

References

[1] Verma, M., Verma, A. K., & Misra, A. K. (2021). Mathematical modeling and optimal control of carbon dioxide emissions from energy sector. Environment, Development and Sustainability, 23(9), 13919-13944.

[2] Shafeeyan, M. S., Daud, W. M. A. W., & Shamiri, A. (2014). A review of mathematical mod eling of fixed-bed columns for carbon dioxide adsorption. Chemical engineering research and design, 92(5), 961-988.

[3] Liu, C. C. (2007). An extended method for key factors in reducing CO2 emissions. Applied Mathematics and Computation, 189(1), 440-451.

[4] Liddle, B. (2015). What are the carbon emissions elasticities for income and population? Bridging STIRPAT and EKC via robust heterogeneous panel estimates. Global Environmen tal Change, 31, 62-73.

[5] Verma, M., Verma, A. K., & Misra, A. K. (2021). Mathematical modeling and optimal control of carbon dioxide emissions from energy sector. Environment, Development and Sustainability, 23(9), 13919-13944.

[6] Mehdipourghazi, M., Barati, S., & Varaminian, F. (2015). Mathematical modeling and sim ulation of carbon dioxide stripping from water using hollow fiber membrane contactors. Chemical Engineering and Processing: Process Intensification, 95, 159-164.

[7] Verma, M., Verma, A. K., & Gautam, C. (2023). Mathematical modeling of mitigation of carbon dioxide emissions by controlling the population pressure. Journal of Engineering Mathematics, 142(1), 2.

[8] Tandon, A. (2023). Mathematical modelling and analysis to study the impact of mining on natural interactive dynamics between plants and carbon dioxide. Modeling Earth Systems and Environment, 9(1), 97-110.

[9] Misra, A. K., & Verma, M. (2013). A mathematical model to study the dynamics of carbon dioxide gas in the atmosphere. Applied Mathematics and Computation, 219(16), 8595-8609.

49

[10] Pomprapa, A., Schwaiberger, D., Lachmann, B., & Leonhardt, S. (2014). A mathematical model for carbon dioxide elimination: an insight for tuning mechanical ventilation. Euro pean journal of applied physiology, 114, 165-175.

[11] Nisar, K. S., Farman, M., Hincal, E., Hasan, A., & Abbas, P. (2024). Chlamydia infection with vaccination asymptotic for qualitative and chaotic analysis using the generalized fractal fractional operator. Scientific Reports, 14(1), 25938.

[12] Barak, M. S., & Gupta, V. (2024). Memory-dependent and fractional order analysis of the initially stressed piezo-thermoelastic medium. Mechanics of Advanced Materials and Struc tures, 31(20), 5013-5027.

[13] Xu, C., Farman, M., Shehzad, A., & Sooppy Nisar, K. (2024). Modeling and UlamHyers stability analysis of oleic acid epoxidation by using a fractional-order kinetic model. Math ematical Methods in the Applied Sciences.

[14] Naik, P. A., Yavuz, M., Qureshi, S., Owolabi, K. M., Soomro, A., & Ganie, A. H. (2024). Memory impacts in hepatitis C: A global analysis of a fractional-order model with an effec tive treatment. Computer Methods and Programs in Biomedicine, 254, 108306.

[15] Nisar, K. S., Farman, M., Abdel-Aty, M., & Ravichandran, C. (2024). A review of fractional order epidemic models for life sciences problems: Past, present and future. Alexandria En gineering Journal, 95, 283-305.

[16] Olayiwola, M. O., Alaje, A. I., & Yunus, A. O. (2024). A Caputo fractional order financial mathematical model analyzing the impact of an adaptive minimum interest rate and maxi mum investment demand. Results in Control and Optimization, 14, 100349.

[17] Benbouhenni, H., Bizon, N., Mosaad, M. I., Colak, I., Djilali, A. B., & Gasmi, H. (2024). Enhancement of the power quality of DFIG-based dual-rotor wind turbine systems using fractional order fuzzy controller. Expert Systems with Applications, 238, 121695.

[18] Farman, M., Gokbulut, N., Hurdoganoglu, U., Hincal, E., & Suer, K. (2024). Fractional order model of MRSA bacterial infection with real data fitting: Computational Analysis and Modeling. Computers in Biology and Medicine, 173, 108367.

[19] Khirsariya, S. R., Rao, S. B., & Hathiwala, G. S. (2024). Investigation of fractional diabetes model involving glucoseinsulin alliance scheme. International Journal of Dynamics and Control, 12(1), 1-14.

[20] Baleanu, D., Jassim, H. K., Ahmed, H., Singh, J., Kumar, D., Shah, R., ... & Jabbar, K. A. (2024). A Mathematical Theoretical Study of Atangana-Baleanu Fractional Burger’s Equa tions. Partial Differential Equations in Applied Mathematics, 100741.

[21] Li, H. L., Cao, J., Hu, C., Jiang, H., & Alsaedi, A. (2024). Synchronization analysis of nabla fractional-order fuzzy neural networks with time delays via nonlinear feedback con trol. Fuzzy Sets and Systems, 475, 108750.

[22] Jassim, H., Ahmed, H., Hussein, M., Singh, J., Kumar, D., Shah, R., ... & Jabbar, K. (2024). On Efficient Method For Fractional-Order Two-Dimensional Navier-Stokes Equations. Iraqi Journal of Science, 5710-5726.

[23] Cheng, W., & Yin, Z. Y. (2024). Fractional order viscoplastic modeling of anisotropically overconsolidated clays with modified isotach viscosity. International Journal of Plasticity, 172, 103858.

50

[24] Nisar, K. S., Ahmad, A., Farman, M., Hincal, E., & Zehra, A. (2024). Modeling and mathe matical analysis of fractional order Eye infection (conjunctivitis) virus model with treatment impact: Prelicence and dynamical transmission. Alexandria Engineering Journal, 107, 33- 46.

[25] Hu, C., & Ji, Y. (2024). Filtering-based gradient joint identification algorithms for nonlin ear fractional-order models with colored noises. Communications in Nonlinear Science and Numerical Simulation, 130, 107759.

[26] Khan, H., Aslam, M., Rajpar, A. H., Chu, Y. M., Etemad, S., Rezapour, S., & Ahmad, H. (2024). A new fractal-fractional hybrid model for studying climate change on coastal ecosystems from the mathematical point of view. Fractals, 32(02), 2440015.

[27] Farman, M., Shehzad, A., Nisar, K. S., Hincal, E., Akgul, A., & Hassan, A. M. (2023). ¨ Generalized Ulam-Hyers-Rassias stability and novel sustainable techniques for dynamical analysis of global warming impact on ecosystem. Scientific Reports, 13(1), 22441.

[28] Premakumari, R. N., Baishya, C., Sajid, M., & Naik, M. K. (2024). Modeling the dynamics of a marine system using the fractional order approach to assess its susceptibility to global warming. Results in Nonlinear Analysis, 7(1), 89-109.

[29] Farman, M., Jamil, K., Xu, C., Nisar, K. S., & Amjad, A. (2025). Fractional order forestry resource conservation model featuring chaos control and simulations for toxin activity and human-caused fire through modified ABC operator. Mathematics and Computers in Simula tion, 227, 282-302.

[30] Gu, H., & Wu, L. (2024). Pulse fractional grey model application in forecasting global carbon emission. Applied Energy, 358, 122638.

[31] Li, C., Qian, D., & Chen, Y. (2011). On Riemann-Liouville and caputo derivatives. Discrete Dynamics in Nature and Society, 2011(1), 562494.

[32] Baleanu, D., Fernandez, A., & Akgul, A. (2020). On a fractional operator combining pro- ¨ portional and classical differintegrals. Mathematics, 8(3), 360.

[33] Akgul, A. (2022). Some Fractional Derivatives with Different Kernels. ¨ International Journal of Applied and Computational Mathematics, 8(4), 183.

[34] Azeem, M., Farman, M., Shehzad, A., & Nisar, K. S. (2024). Hybrid fractional derivative for modeling and analysis of cancer treatment with virotherapy. Stochastic Analysis and Applications, 1-33.

[35] Naik, P. A., Zehra, A., Farman, M., Shehzad, A., Shahzeen, S., & Huang, Z. (2024). Fore casting and dynamical modeling of reversible enzymatic reactions with a hybrid proportional fractional derivative. Frontiers in Physics, 11, 1307307.

[36] Ali, R., Akgul, A., & Asjad, M. I. (2020). Power law memory of natural convection flow ¨ of hybrid nanofluids with constant proportional Caputo fractional derivative due to pressure gradient. Pramana, 94(1), 131.

[37] Xu, C., & Farman, M. (2023). Dynamical transmission and mathematical analysis of Ebola virus using a constant proportional operator with a power law kernel. Fractal and Fractional, 7(10), 706.

51

[38] Chen, L., Hussain, D., Sun, B., Kazim, M., & Abbas, M. A. (2024). Optimization of mass and heat flux of MHD viscous fluid flow with constant proportional Caputo derivative by using response surface methodology: Sensitivity analysis. International Communications in Heat and Mass Transfer, 154, 107442.

[39] Naik, P. A., Zehra, A., Farman, M., Shehzad, A., Shahzeen, S., & Huang, Z. (2024). Fore casting and dynamical modeling of reversible enzymatic reactions with a hybrid proportional fractional derivative. Frontiers in Physics, 11, 1307307.

[40] Nisar, K. S., Farman, M., Hincal, E., & Shehzad, A. (2023). Modelling and analysis of bad impact of smoking in society with Constant Proportional-Caputo Fabrizio operator. Chaos, Solitons & Fractals, 172, 113549.