Abstract
We study gross domestic product (GDP) model utilizing Atangana–Baleanu, Caputo–Fabrizio and Caputo fractional derivatives under the light of real data of the United Kingdom given by World Bank (World development indicators, 2018) between years 1972–2007. We obtain analytical solutions of fractional models by using Laplace transform. We compare the GDP results obtained for different fractional derivatives with real data by simulations and tables with statistical analysis showing the efficiency of fractional models to the integer-order counterpart employing error sum of squares and residual sum of squares.
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References
Abdeljawad T (2017) Fractional operators with exponential kernels and a Lyapunov type inequality. Adv Differ Equ 2017(1):313
Abdeljawad T, Baleanu D (2017a) Integration by parts and its applications of a new nonlocal fractional derivative with Mittag–Leffler nonsingular kernel. J Nonlinear Sci Appl 10(3):1098–1107
Abdeljawad T, Baleanu D (2017b) On fractional derivatives with exponential kernel and their discrete versions. Rep Math Phys 80(1):11–27
Al-Refai M, Abdeljawad T (2017) Analysis of the fractional diffusion equations with fractional derivative of non-singular kernel. Adv Differ Equ 2017(1):315
Almeida R, Bastos NR, Monteiro MTT (2016) Modeling some real phenomena by fractional differential equations. Math Methods Appl Sci 39(16):4846–4855
Alsaedi A, Baleanu D, Etemad S, Rezapour S (2016) On coupled systems of time-fractional differential problems by using a new fractional derivative. J Funct Sp 1:1–9
Atangana A, Alqahtani RT (2016) Numerical approximation of the space-time caputo-fabrizio fractional derivative and application to groundwater pollution equation. Adv Differ Equ 2016(1):1–13
Atangana A, Baleanu D (2016) New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model. Therm Sci 20(2):763–769
Atangana A, Baleanu D (2017) Caputo–Fabrizio derivative applied to groundwater flow within confined aquifer. J Eng Mech 143(5):D4016005
Atangana A, Koca I (2016) Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order. Chaos Solitons Fractals 89:447–454
Bas E (2015) The inverse nodal problem for the fractional diffusion equation. Acta Sci. Technol. 37(2):251–257
Bas E, Ozarslan R (2019) Theory of discrete fractional Sturm–Liouville equations and visual results. AIMS Math. 4(3):593–612
Bas E, Acay B, Ozarslan R (2019) The price adjustment equation with different types of conformable derivatives in market equilibrium. AIMS Math. 4(3):593–612
Caputo M, Fabrizio M (2015) A new definition of fractional derivative without singular kernel. Progr. Fract. Differ. Appl 1(2):1–13
Chen W-C (2008) Nonlinear dynamics and chaos in a fractional-order financial system. Chaos Solitons Fractals 36(5):1305–1314
Gómez-Aguilar J, Atangana A (2017) New insight in fractional differentiation: power, exponential decay and Mittag–Leffler laws and applications. Eur Phys J Plus 132(1):13
Gómez-Aguilar JF, Morales-Delgado VF, Taneco-Hernández MA, Baleanu D, Escobar-Jiménez RF, Al Qurashi MM (2016) Analytical solutions of the electrical RLC circuit via Liouville–Caputo operators with local and non-local kernels. Entropy 18(8):402
Gómez-Aguilar JF, Atangana A, Morales-Delgado VF (2017) Electrical circuits RC, LC, and RL described by Atangana–Baleanu fractional derivatives. Int J Circuit Theory Appl 45(11):1514–1533
Jarad F, Uğurlu E, Abdeljawad T, Baleanu D (2017) On a new class of fractional operators. Adv Differ Equ 2017(1):247
Kanth AR, Garg N (2018) Computational simulations for solving a class of fractional models via Caputo–Fabrizio fractional derivative. Procedia Comput Sci 125:476–482
Kuroda LKB, Gomes AV, Tavoni R, de Arruda Mancera PF, Varalta N, de Figueiredo Camargo R (2017) Unexpected behavior of Caputo fractional derivative. Comput Appl Math 36(3):1173–1183
Owolabi KM, Atangana A (2017) Numerical approximation of nonlinear fractional parabolic differential equations with Caputo–Fabrizio derivative in Riemann–Liouville sense. Chaos Solitons Fractals 99:171–179
Ozarslan R, Ercan A, Bas E (2019) \(\beta \)-Type fractional Sturm–Liouville coulomb operator and applied results. Math Methods Appl Sci 42(18):6648–6659
Podlubny I (1998) Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Elsevier, New York
Sun H, Hao X, Zhang Y, Baleanu D (2017) Relaxation and diffusion models with non-singular kernels. Phys A Stat Mech Appl 468:590–596
Uğurlu E, Baleanu D, TAŞ K (2018) On the solutions of a fractional boundary value problem. Turk J Math 42(3):1307–1311
Varalta N, Gomes AV, Camargo RdF (2014) A prelude to the fractional calculus applied to tumor dynamic. TEMA (São Carlos) 15(2):211–221
World Bank (2018) World Development Indicators. Accessed 25 July 25 2018
Yavuz M, Ozdemir N, Baskonus HM (2018) Solutions of partial differential equations using the fractional operator involving Mittag–Leffler kernel. Eur Phys J Plus 133(6):215
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Ozarslan, R., Bas, E. Reassessments of gross domestic product model for fractional derivatives with non-singular and singular kernels. Soft Comput 25, 1535–1541 (2021). https://doi.org/10.1007/s00500-020-05237-4
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DOI: https://doi.org/10.1007/s00500-020-05237-4