[1] Elnady, S.M., El-Beltagy, M., Radwan, A.G., Fouda, M., A generalized local fractional derivative with applications, Journal of Computational Physics, 530, 2025, 113903.
[2] Teodoro, G.S., Machado, J..T., De Oliveira, E.C., A review of definitions of fractional derivatives and other operators, Journal of Computational Physics, 388, 2019, 195–208.
[3] Sonin, N.Y., On differentiation with arbitrary index, Moscow Matem. Sbornik, 6, 1869, 1–8.
[4] Liouville, J., Sur le calcul des differentielles á indices quelconques (in french), j, volume 71, 1832.
[5] Gerasimov, A.N., A generalization of linear laws of deformation and its application to problems of internal friction, Akad. Nauk SSSR. Prikl. Mat. Meh, 12, 1948, 251–260.
[6] Caputo, M., Linear models of dissipation whose Q is almost frequency independent-ii, Geophysical Journal of the Royal Astronomical Society, 13, 1967, 529–539.
[7] Caputo, M., Elasticita e dissipazione, Zanichelli, 1969.
[8] Dzherbashian, M.M., Nersesian, A.B., Fractional derivatives and the cauchy problem for differential equations of fractional order, Izv. Akad. Nauk Armenian SSR Matem, 3, 1968, 3–28.
[9] De Oliveira, E.C., Machado, J.A., A review of definitions for fractional derivatives and integral, Mathematical Problems in Engineering, 2014, 2014, 1–7.
[10] Almeida, R., A Caputo fractional derivative of a function with respect to another function, Communications in Nonlinear Science and Numerical Simulation, 44, 2017, 460–481.
[11] Almeida, R., Caputo-Hadamard fractional derivatives of variable order, Numerical Functional Analysis and Optimization, 38, 2017, 1–19.
[12] Oliveira, D.S., De Oliveira, E.C., On a Caputo-type fractional derivative, Advances in Pure and Applied Mathematics, 10, 2019, 81–91.
[13] Oliveira, D.S., De Oliveira, E.C., Hilfer-Katugampola fractional derivatives, Computational and Applied Mathematics, 37, 2018, 3672–3690.
[14] Oliveira, D.S., de Oliveira, E.C., On the generalized (k, ρ)-fractional derivative, Progress in Fractional Differentiation and Applications, 4, 2018, 133–145.
[15] Sousa, J.V.d.C., De Oliveira, E.C., On the ψ-Hilfer fractional derivative, Commun. Nonlinear Sci. Numer. Simul, 60, 2018, 72–91.
[16] Kilbas, A.A., Srivastava, H.M., Trujillo, J.J., Theory and applications of fractional differential equations, volume 204, North-Holland Mathematics Studies, 2006.
[17] Katugampola, U.N., New approach to a generalized fractional integral, Applied Mathematics and Computation, 218, 2011, 860–865.
[18] Khalil, R., Al Horani, M., Yousef, A., Sababheh, M., A new definition of fractional derivative, Journal of Computational and Applied Mathematics, 264, 2014, 65–70.
[19] Zhao, D., Luo, M., General conformable fractional derivative and its physical interpretation, Calcolo, 54, 2017, 903–917.
[20] Caputo, M., Fabrizio, M., A new definition of fractional derivative without singular kernel, Progress in Fractional Differentiation and Applications, 1, 2015, 73–85.
[21] Ortigueira, M.D., Machado, J.T., A critical analysis of the Caputo-Fabrizio operator, Communications in Nonlinear Science and Numerical Simulation, 59, 2018, 608–611.
[22] Losada, J., Nieto, J.J., Properties of a new fractional derivative without singular kernel, Progress in Fractional Differentiation and Applications, 1, 2015, 87–92.
[23] Atangana, A., On the new fractional derivative and application to nonlinear Fisher’s reaction–diffusion equation, Applied Mathematics and Computation, 273, 2016, 948–956.
[24] Atangana, A., Baleanu, D., New fractional derivatives with non-local and non-singular kernel: Theory and application to heat transfer model, Thermal Science, 20, 2016, 763–769.
[25] Podlubny, I., An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, volume 198, Academic Press, San Diego, California, 92101-4495, USA, 1999.
[26] Wang, K.J., A new fractional nonlinear singular heat conduction model for the human head considering the effect of febrifuge, The European Physical Journal Plus, 135, 2020, 871.
[27] He, J.H., A tutorial review on fractal spacetime and fractional calculus, International Journal of Theoretical Physics, 53, 2014, 3698–3718.
[28] He, J.H., Fractal calculus and its geometrical explanation, Results in Physics, 10, 2018, 272–276.
[29] Abdelhakim, A.A., The flaw in the conformable calculus: It is conformable because it is not fractional, Fractional Calculus and Applied Analysis, 22, 2019, 242–254.
[30] Katugampola, U.N., Correction to “what is a fractional derivative?” by Ortigueira and Machado [Journal of Computational Physics, volume 293, 15 july 2015, pages 4-13. Special issue on Fractional PDEs], Journal of Computational Physics, 321, 2016, 1255–1257.
[31] Chang, S.H., Taylor series method for solving a class of nonlinear singular boundary value problems arising in applied science, Applied Mathematics and Computation, 235, 2014, 110–117.
[32] He, J.H., Ji, F.Y., Taylor series solution for Lane-Emden equation, Journal of Mathematical Chemistry, 57, 2019, 1932–1934.
[33] He, J.H., Verma, L., Pandit, B., Verma, A.K., Agarwal, R.P., A new Taylor series based numerical method: Simple, reliable, and promising, Journal of Applied and Computational Mechanics, 9, 2023, 1122–1134.
[34] Verma, A.K., Pandit, B., Verma, L., Agarwal, R.P., A review on a class of second order nonlinear singular BVPs, Mathematics, 8, 2020, 1045.
[35] Katugampola, U.N., A new fractional derivative with classical properties, arXiv, arXiv:1410.6535.
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