How to cite this paper
Johansyah, M., Nahar, J., Djauhari, E., Napitupulu, H & Saputra, J. (2022). Determining the price elasticity of demand with and without memory effects using fractional order derivatives: A numerical simulation approach.Decision Science Letters , 11(3), 311-322.
Refrences
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Andruszkiewicz, J., Lorenc, J., & Weychan, A. (2019). Demand price elasticity of residential electricity consumers with zonal tariff settlement based on their load profiles. Energies, 12(22), 4317.
Andruszkiewicz, J., Lorenc, J., & Weychan, A. (2020). Seasonal variability of price elasticity of demand of households using zonal tariffs and its impact on hourly load of the power system. Energy, 196, 117175.
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Baleanu, D., & Agarwal, R. P. (2021). Fractional calculus in the sky. Advances in Difference Equations, 2021(1), 117. Retrieved from https://doi.org/10.1186/s13662-021-03270-7
Chen, S.-B., Rashid, S., Noor, M. A., Ashraf, R., & Chu, Y.-M. (2020). A new approach on fractional calculus and probability density function. AIMS Mathematics, 5(6), 7041–7054.
Diethelm, K., & Ford, N. J. (2002). Analysis of fractional differential equations. Journal of Mathematical Analysis and Applications, 265(2), 229–248.
Fang, J. (2020). Prediction and analysis of regional economic income multiplication capability based on fractional accumulation and integral model. Chaos, Solitons & Fractals, 130, 109441.
Khan, M. A., Azizah, M., & Ullah, S. (2019). A fractional model for the dynamics of competition between commercial and rural banks in Indonesia. Chaos, Solitons & Fractals, 122, 32–46.
Kim, G.-S., & Kwak, K.-S. (2004). The Price Elasticity in the Parcel Service Market by Benefit Segmentation. Journal of Korean Society of Transportation, 22(2), 7–18.
Ma, J., & Ren, W. (2016). Complexity and Hopf bifurcation analysis on a kind of fractional-order IS-LM macroeconomic system. International Journal of Bifurcation and Chaos, 26(11), 1650181.
Machado, J. A. T., & Mata, M. E. (2015). Pseudo phase plane and fractional calculus modeling of western global economic downturn. Communications in Nonlinear Science and Numerical Simulation, 22(1–3), 396–406.
Ming, H., Wang, J., & Fečkan, M. (2019). The application of fractional calculus in Chinese economic growth models. Mathematics, 7(8), 665.
Petricek, M., Chalupa, S., & Chadt, K. (2020). Identification of consumer behavior based on price elasticity: A case study of the Prague market of accommodation services. Sustainability, 12(22), 9452.
Rahaman, M., Mondal, S. P., Shaikh, A. A., Pramanik, P., Roy, S., Maiti, M. K., … De, D. (2020). Artificial bee colony optimization-inspired synergetic study of fractional-order economic production quantity model. Soft Computing, 24(20), 15341–15359.
Rashid, M., & Mitra, D. (1999). Price elasticity of demand and an optimal cash discount rate in credit policy. Financial Review, 34(3), 113–125.
Sambas, A., He, S., Liu, H., Vaidyanathan, S., Hidayat, Y., & Saputra, J. (2020). Dynamical analysis and adaptive fuzzy control for the fractional-order financial risk chaotic system. Advances in Difference Equations, 2020(1), 1–12.
Sambas, A., Vaidyanathan, S., Bonny, T., Zhang, S., Hidayat, Y., Gundara, G., & Mamat, M. (2021). Mathematical model and FPGA realization of a multi-stable chaotic dynamical system with a closed butterfly-like curve of equilibrium points. Applied Sciences, 11(2), 788.
Sambas, A., Vaidyanathan, S., Tlelo-Cuautle, E., Abd-El-Atty, B., Abd El-Latif, A. A., Guillén-Fernández, O., … Gundara, G. (2020). A 3-D multi-stable system with a peanut-shaped equilibrium curve: Circuit design, FPGA realization, and an application to image encryption. IEEE Access, 8, 137116–137132.
Škovránek, T., Podlubny, I., & Petráš, I. (2012). Modeling of the national economies in state-space: A fractional calculus approach. Economic Modelling, 29(4), 1322–1327.
Sukawattanapornkul, A., Siritaratiwat, A., Khunkitti, P., Surawanitkun, C., & Chatthaworn, R. (2019). The Novel Price Elasticity of Demand Model for Time of Use Electricity Rates Determination. International Journal of Engineering Research and Technology, 12 (10) (2019), 1799-1807, 12(10), 1799–1807.
Tarasova, V. V, & Tarasov, V. E. (2016). Elasticity for economic processes with memory: Fractional differential calculus approach. Fractional Differential Calculus, 6(2), 219–232.
Tejado, I, Perez, E., & Valerio, D. (2018). Economic growth in the European Union modelled with fractional derivatives: First results. Bulletin of the Polish Academy of Sciences. Technical Sciences, 66(4).
Tejado, Inés, Valério, D., & Valério, N. (2014). Fractional calculus in economic growth modeling. The Portuguese case. In ICFDA’14 International Conference on Fractional Differentiation and Its Applications 2014 (pp. 1–6). IEEE.
Tejado, Inés, Valério, D., & Valério, N. (2015). Fractional calculus in economic growth modelling: The spanish case. In CONTROLO’2014–Proceedings of the 11th Portuguese Conference on Automatic Control (pp. 449–458). Springer.
Vaidyanathan, S., Feki, M., Sambas, A., & Lien, C.-H. (2018). A new biological snap oscillator: its modelling, analysis, simulations and circuit design. International Journal of Simulation and Process Modelling, 13(5), 419–432.
Vaidyanathan, S., Sambas, A., Kacar, S., & Cavusoglu, U. (2019). A new finance chaotic system, its electronic circuit realization, passivity based synchronization and an application to voice encryption. Nonlinear Engineering, 8(1), 193–205.
Xie, Y., Wang, Z., & Meng, B. (2019). Stability and bifurcation of a delayed time-fractional order business cycle model with a general liquidity preference function and investment function. Mathematics, 7(9), 846.
Xin, B., & Li, Y. (2013). 0-1 test for chaos in a fractional order financial system with investment incentive. In Abstract and Applied Analysis (Vol. 2013). Hindawi.
Xin, B., & Zhang, J. (2015). Finite-time stabilizing a fractional-order chaotic financial system with market confidence. Nonlinear Dynamics, 79(2), 1399–1409.
Zhang, J., Fu, X., & Morris, H. (2019). Construction of indicator system of regional economic system impact factors based on fractional differential equations. Chaos, Solitons & Fractals, 128, 25–33.
Andruszkiewicz, J., Lorenc, J., & Weychan, A. (2019). Demand price elasticity of residential electricity consumers with zonal tariff settlement based on their load profiles. Energies, 12(22), 4317.
Andruszkiewicz, J., Lorenc, J., & Weychan, A. (2020). Seasonal variability of price elasticity of demand of households using zonal tariffs and its impact on hourly load of the power system. Energy, 196, 117175.
Babbel, D. F. (1985). The price elasticity of demand for whole life insurance. The Journal of Finance, 40(1), 225–239.
Baleanu, D., & Agarwal, R. P. (2021). Fractional calculus in the sky. Advances in Difference Equations, 2021(1), 117. Retrieved from https://doi.org/10.1186/s13662-021-03270-7
Chen, S.-B., Rashid, S., Noor, M. A., Ashraf, R., & Chu, Y.-M. (2020). A new approach on fractional calculus and probability density function. AIMS Mathematics, 5(6), 7041–7054.
Diethelm, K., & Ford, N. J. (2002). Analysis of fractional differential equations. Journal of Mathematical Analysis and Applications, 265(2), 229–248.
Fang, J. (2020). Prediction and analysis of regional economic income multiplication capability based on fractional accumulation and integral model. Chaos, Solitons & Fractals, 130, 109441.
Khan, M. A., Azizah, M., & Ullah, S. (2019). A fractional model for the dynamics of competition between commercial and rural banks in Indonesia. Chaos, Solitons & Fractals, 122, 32–46.
Kim, G.-S., & Kwak, K.-S. (2004). The Price Elasticity in the Parcel Service Market by Benefit Segmentation. Journal of Korean Society of Transportation, 22(2), 7–18.
Ma, J., & Ren, W. (2016). Complexity and Hopf bifurcation analysis on a kind of fractional-order IS-LM macroeconomic system. International Journal of Bifurcation and Chaos, 26(11), 1650181.
Machado, J. A. T., & Mata, M. E. (2015). Pseudo phase plane and fractional calculus modeling of western global economic downturn. Communications in Nonlinear Science and Numerical Simulation, 22(1–3), 396–406.
Ming, H., Wang, J., & Fečkan, M. (2019). The application of fractional calculus in Chinese economic growth models. Mathematics, 7(8), 665.
Petricek, M., Chalupa, S., & Chadt, K. (2020). Identification of consumer behavior based on price elasticity: A case study of the Prague market of accommodation services. Sustainability, 12(22), 9452.
Rahaman, M., Mondal, S. P., Shaikh, A. A., Pramanik, P., Roy, S., Maiti, M. K., … De, D. (2020). Artificial bee colony optimization-inspired synergetic study of fractional-order economic production quantity model. Soft Computing, 24(20), 15341–15359.
Rashid, M., & Mitra, D. (1999). Price elasticity of demand and an optimal cash discount rate in credit policy. Financial Review, 34(3), 113–125.
Sambas, A., He, S., Liu, H., Vaidyanathan, S., Hidayat, Y., & Saputra, J. (2020). Dynamical analysis and adaptive fuzzy control for the fractional-order financial risk chaotic system. Advances in Difference Equations, 2020(1), 1–12.
Sambas, A., Vaidyanathan, S., Bonny, T., Zhang, S., Hidayat, Y., Gundara, G., & Mamat, M. (2021). Mathematical model and FPGA realization of a multi-stable chaotic dynamical system with a closed butterfly-like curve of equilibrium points. Applied Sciences, 11(2), 788.
Sambas, A., Vaidyanathan, S., Tlelo-Cuautle, E., Abd-El-Atty, B., Abd El-Latif, A. A., Guillén-Fernández, O., … Gundara, G. (2020). A 3-D multi-stable system with a peanut-shaped equilibrium curve: Circuit design, FPGA realization, and an application to image encryption. IEEE Access, 8, 137116–137132.
Škovránek, T., Podlubny, I., & Petráš, I. (2012). Modeling of the national economies in state-space: A fractional calculus approach. Economic Modelling, 29(4), 1322–1327.
Sukawattanapornkul, A., Siritaratiwat, A., Khunkitti, P., Surawanitkun, C., & Chatthaworn, R. (2019). The Novel Price Elasticity of Demand Model for Time of Use Electricity Rates Determination. International Journal of Engineering Research and Technology, 12 (10) (2019), 1799-1807, 12(10), 1799–1807.
Tarasova, V. V, & Tarasov, V. E. (2016). Elasticity for economic processes with memory: Fractional differential calculus approach. Fractional Differential Calculus, 6(2), 219–232.
Tejado, I, Perez, E., & Valerio, D. (2018). Economic growth in the European Union modelled with fractional derivatives: First results. Bulletin of the Polish Academy of Sciences. Technical Sciences, 66(4).
Tejado, Inés, Valério, D., & Valério, N. (2014). Fractional calculus in economic growth modeling. The Portuguese case. In ICFDA’14 International Conference on Fractional Differentiation and Its Applications 2014 (pp. 1–6). IEEE.
Tejado, Inés, Valério, D., & Valério, N. (2015). Fractional calculus in economic growth modelling: The spanish case. In CONTROLO’2014–Proceedings of the 11th Portuguese Conference on Automatic Control (pp. 449–458). Springer.
Vaidyanathan, S., Feki, M., Sambas, A., & Lien, C.-H. (2018). A new biological snap oscillator: its modelling, analysis, simulations and circuit design. International Journal of Simulation and Process Modelling, 13(5), 419–432.
Vaidyanathan, S., Sambas, A., Kacar, S., & Cavusoglu, U. (2019). A new finance chaotic system, its electronic circuit realization, passivity based synchronization and an application to voice encryption. Nonlinear Engineering, 8(1), 193–205.
Xie, Y., Wang, Z., & Meng, B. (2019). Stability and bifurcation of a delayed time-fractional order business cycle model with a general liquidity preference function and investment function. Mathematics, 7(9), 846.
Xin, B., & Li, Y. (2013). 0-1 test for chaos in a fractional order financial system with investment incentive. In Abstract and Applied Analysis (Vol. 2013). Hindawi.
Xin, B., & Zhang, J. (2015). Finite-time stabilizing a fractional-order chaotic financial system with market confidence. Nonlinear Dynamics, 79(2), 1399–1409.
Zhang, J., Fu, X., & Morris, H. (2019). Construction of indicator system of regional economic system impact factors based on fractional differential equations. Chaos, Solitons & Fractals, 128, 25–33.