Adaptation of conformable residual series algorithm for solving temporal fractional gas dynamics models

References

• Abdeljawad, T. (2015). On conformable fractional calculus. Journal of Computational and Applied Mathematics, 279, 57–66. doi:10.1016/j.cam.2014.10.016
   Web of Science ®Google Scholar
• Abdeljawad, T. (2019). Fractional difference operators with discrete generalized Mittag-Leffler kernels. Chaos, Solitons and Fractals, 126, 315–324. doi:10.1016/j.chaos.2019.06.012
   Web of Science ®Google Scholar
• Abu Arqub, O., & Al-Smadi, M. (2020a). An adaptive numerical approach for the solutions of fractional advection-diffusion and dispersion equations in singular case under Riesz's derivative operator. Physica A: Statistical Mechanics and Its Applications, 540, 123257. doi:10.1016/j.physa.2019.123257
   Web of Science ®Google Scholar
• Abu Arqub, O., & Al-Smadi, M. (2020b). Fuzzy conformable fractional differential equations: Novel extended approach and new numerical solutions. Soft Computing, 24(16), 12501–12522. doi:10.1007/s00500-020-04687-0
   Web of Science ®Google Scholar
• Abu Arqub, O., Al-Smadi, M., Almusawa, H., Baleanu, D., Hayat, T., Alhodaly, M., & Osman, M.S. (2022). A novel analytical algorithm for generalized fifth-order time-fractional nonlinear evolution equations with conformable time derivative arising in shallow water waves. Alexandria Engineering Journal, 61(7), 5753–5769. doi:10.1016/j.aej.2021.12.044
   Web of Science ®Google Scholar
• Abu Arqub, O., Odibat, Z., & Al-Smadi, M. (2018). Numerical solutions of time-fractional partial integrodifferential equations of Robin functions types in Hilbert space with error bounds and error estimates. Nonlinear Dynamics, 94(3), 1819–1834. doi:10.1007/s11071-018-4459-8
   Web of Science ®Google Scholar
• Acan, O., & Baleanu, D. (2018). A new numerical technique for solving fractional partial differential equations. Miskolc Mathematical Notes, 19(1), 3–18. doi:10.18514/MMN.2018.2291
   Web of Science ®Google Scholar
• Agarwal, P., Baleanu, D., Chen, Y.Q., Momani, S., & Machado, J.A.T. (2019). Fractional calculus. ICFDA 2018. Springer Proceedings in Mathematics & Statistics, vol. 303. Springer, Singapore.
   Google Scholar
• Akram, T., Abbas, M., Riaz, M.B., Ismail, A.I., & Ali, N.M. (2020). An efficient numerical technique for solving time fractional Burgers equation. Alexandria Engineering Journal, 59(4), 2201–2220. doi:10.1016/j.aej.2020.01.048
   Web of Science ®Google Scholar
• Al-Deiakeh, R., Abu Arqub, O., Al-Smadi, M., & Momani, S. (2021). Lie symmetry analysis, explicit solutions, and conservation laws of the time-fractional Fisher equation in two-dimensional space. Journal of Ocean Engineering and Science, in press. doi:10.1016/j.joes.2021.09.005
   Web of Science ®Google Scholar
• Allahviranloo T, Salahshour S, Abbasbandy, S. (2012). Explicit solutions of fractional differential equations with uncertainty. Soft Computing, 16(2), 297–302. doi:10.1007/s00500-011-0743-y
   Web of Science ®Google Scholar
• Al-Smadi, M. (2021). Fractional residual series for conformable time-fractional Sawada-Kotera-Ito, Lax, and Kaup-Kupershmidt equations of seventh-order. Mathematical Methods in the Applied Sciences. doi:10.1002/mma.7507
   Google Scholar
• Al-Smadi, M., & Abu Arqub, O. (2019). Computational algorithm for solving fredholm time-fractional partial integrodifferential equations of dirichlet functions type with error estimates. Applied Mathematics and Computation, 342, 280–294. doi:10.1016/j.amc.2018.09.020
   Web of Science ®Google Scholar
• Al-Smadi, M., Abu Arqub, O., & Gaith, M. (2021). Numerical simulation of telegraph and Cattaneo fractional-type models using adaptive reproducing kernel framework. Mathematical Methods in the Applied Sciences, 44(10), 8472–8489. doi:10.1002/mma.6998
   Web of Science ®Google Scholar
• Al-Smadi, M., Abu Arqub, O., & Hadid, S. (2020a). An attractive analytical technique for coupled system of fractional partial differential equations in shallow water waves with conformable derivative. Communications in Theoretical Physics, 72(8), 085001. doi:10.1088/1572-9494/ab8a29
   Web of Science ®Google Scholar
• Al-Smadi, M., Abu Arqub, O., & Hadid, S. (2020b). Approximate solutions of nonlinear fractional Kundu-Eckhaus and coupled fractional massive Thirring equations emerging in quantum field theory using conformable residual power series method. Physica Scripta, 95(10), 105205. doi:10.1088/1402-4896/abb420
   Web of Science ®Google Scholar
• Al-Smadi, M., Abu Arqub, O., & Momani, S. (2020). Numerical computations of coupled fractional resonant Schrödinger equations arising in quantum mechanics under conformable fractional derivative sense. Physica Scripta, 95(7), 075218. doi:10.1088/1402-4896/ab96e0
   Web of Science ®Google Scholar
• Al-Smadi, M., Abu Arqub, O., & Zeidan, D. (2021). Fuzzy fractional differential equations under the Mittag-Leffler kernel differential operator of the ABC approach: Theorems and applications. Chaos, Solitons and Fractals, 146, 110891. doi:10.1016/j.chaos.2021.110891
   Web of Science ®Google Scholar
• Al-Smadi, M., Djeddi, N., Momani, S., Al-Omari, S., & Araci, S. (2021). An attractive numerical algorithm for solving nonlinear Caputo-Fabrizio fractional Abel differential equation in a Hilbert space. Advances in Difference Equations, 2021(1), 271. doi:10.1186/s13662-021-03428-3
   Web of Science ®Google Scholar
• Al-Smadi, M., Dutta, H., Hasan, S., & Momani, S. (2021). On numerical approximation of Atangana-Baleanu-Caputo fractional integro-differential equations under uncertainty in Hilbert Space. Mathematical Modelling of Natural Phenomena, 16, 41. doi:10.1051/mmnp/2021030
   Web of Science ®Google Scholar
• Amryeen, R., Harun, F.N., Al-Smadi, M., & Alias, A. (2020). Adaptation of residual power series approach for solving time-fractional nonlinear Kline-Gordon equations with conformable derivative. Applied Mathematics and Information Sciences, 14(4), 563–575.
   Google Scholar
• Anderson, D.R., & Ulness, D.J. (2015). Newly defined conformable derivatives. Advances in Dynamical Systems and Applications, 10, 109–137.
   Google Scholar
• Arqub, O. A. (2013). Series solution of fuzzy differential equations under strongly generalized differentiability. Journal of Advanced Research in Applied Mathematics, 5, 31–52.
   Google Scholar
• Arqub, O. A. (2019). Application of residual power series method for the solution of time-fractional Schrödinger equations in one-dimensional space. Fundamenta Informaticae, 166(2), 87–110. doi:10.3233/FI-2019-1795
   Web of Science ®Google Scholar
• Atangana, A. (2016). On the new fractional derivative and application to nonlinear Fisher's reaction-diffusion equation. Applied Mathematics and Computation, 273, 948–956. doi:10.1016/j.amc.2015.10.021
   Web of Science ®Google Scholar
• Atangana, A., & Baleanu, D. (2016). New fractional derivatives with non-local and non-singular kernel: Theory and application to heat transfer model. Thermal Science, 20(2), 763–769. doi:10.2298/TSCI160111018A
   Web of Science ®Google Scholar
• Atangana, A., & Gómez-Aguilar, J.F. (2018). Decolonisation of fractional calculus rules: Breaking commutativity and associativity to capture more natural phenomena. The European Physical Journal Plus, 133(4), 1–22. doi:10.1140/epjp/i2018-12021-3
   Web of Science ®Google Scholar
• Atangana, A., & Nieto, J.J. (2015). Numerical solution for the model of RLC circuit via the fractional derivative without singular kernel. Advances in Mechanical Engineering, 7, 1–7.
   Web of Science ®Google Scholar
• Biazar, J., & Eslami, M. (2011). Differential transform method for nonlinear fractional gas dynamics equation. International Journal of the Physical Sciences, 6(5), 1203.
   Google Scholar
• Bira, B., Sekhar, T.R., & Zeidan, D. (2018). Exact solutions for some time‐fractional evolution equations using Lie group theory. Mathematical Methods in the Applied Sciences, 41(16), 6717–6725. doi:10.1002/mma.5186
   Web of Science ®Google Scholar
• Caputo, M., & Fabrizio, M. (2015). A new definition of fractional derivative without singular kernel. Progress in Fractional Differentiation and Applications, 1(2), 73–85.
   Google Scholar
• Das, S., & Kumar, R. (2011). Approximate analytical solutions of fractional gas dynamics. Applied Mathematics and Computation, 217(24), 9905–9915. doi:10.1016/j.amc.2011.03.144
   Web of Science ®Google Scholar
• Hammad, H.A., Agarwal, P., Momani, S., & Alsharari, F. (2021). Solving a fractional-order differential equation using rational symmetric contraction mappings. Fractal and Fractional, 5(4), 159. doi:10.3390/fractalfract5040159
   Web of Science ®Google Scholar
• Hasan, S., Al-Smadi, M., El-Ajou, A., Momani, S., Hadid, S., & Al-Zhour, Z. (2021). Numerical approach in the Hilbert space to solve a fuzzy Atangana-Baleanu fractional hybrid system. Chaos, Solitons & Fractals, 143, 110506. doi:10.1016/j.chaos.2020.110506
   Web of Science ®Google Scholar
• Khalid, N., Abbas, M., Iqbal, M.K., & Baleanu, D. (2020). A numerical investigation of Caputo time fractional Allen–Cahn equation using redefined cubic B-spline functions. Advances in Difference Equations, 2020(1), 158. doi:10.1186/s13662-020-02616-x
   Web of Science ®Google Scholar
• Khalid, N., Abbas, M., Iqbal, M.K., Singh, J., & Md, A.I. (2020). Ismail, A computational approach for solving time fractional differential equation via spline functions. Alexandria Engineering Journal, 59(5), 3061–3078. doi:10.1016/j.aej.2020.06.007
   Web of Science ®Google Scholar
• Khalil, R., Al Horani, M., Yousef, A., & Sababheh, M. (2014). A new definition of fractional derivative. Journal of Computational and Applied Mathematics, 264, 65–70. doi:10.1016/j.cam.2014.01.002
   Web of Science ®Google Scholar
• Kumar, S., & Rashidi, M.M. (2014). New analytical method for gas dynamics equation arising in shock fronts. Computer Physics Communications, 185(7), 1947–1954. doi:10.1016/j.cpc.2014.03.025
   Web of Science ®Google Scholar
• Majeed, A., Kamran, M., Abbas, M., & Bin Misro, M.Y. (2021). An efficient numerical scheme for the simulation of time-fractional nonhomogeneous Benjamin-Bona-Mahony-Burger model. Physica Scripta, 96(8), 084002. doi:10.1088/1402-4896/abfde2
   Web of Science ®Google Scholar
• Miller, K.S., & Ross, B. (1993). An introduction to the fractional calculus and fractional differential equations. New York: Wiley.
   Google Scholar
• Momani, S., Djeddi, N., Al-Smadi, M., & Al-Omari, S. (2021). Numerical investigation for Caputo-Fabrizio fractional Riccati and Bernoulli equations using iterative reproducing kernel method. Applied Numerical Mathematics, 170, 418–434. doi:10.1016/j.apnum.2021.08.005
   Web of Science ®Google Scholar
• Mousa, M.M., Agarwal, P., Alsharari, F., & Momani, S. (2021). Capturing of solitons collisions and reflections in nonlinear Schrödinger type equations by a conservative scheme based on MOL. Advances in Difference Equations, 2021(1), 346. doi:10.1186/s13662-021-03505-7
   Web of Science ®Google Scholar
• Senol, M., Tasbozan, O., & Kurt, A. (2019). Numerical solutions of fractional burgers' type equations with conformable derivative. Chinese Journal of Physics, 58, 75–84. doi:10.1016/j.cjph.2019.01.001
   Web of Science ®Google Scholar
• Shi, L., Khan, M.G., Ahmad, B., Mashwani, W.K., Agarwal, P., & Momani, S. (2021). Certain coefficient estimate problems for three-leaf-type starlike functions. Fractal and Fractional, 5(4), 137. doi:10.3390/fractalfract5040137
   Web of Science ®Google Scholar
• Sunarto, A., Agarwal, P., Sulaiman, J., Chew, J.V.L., & Momani, S. (2021). Quarter-sweep preconditioned relaxation method, algorithm and efficiency analysis for fractional mathematical equation. Fractal and Fractional, 5(3), 98. doi:10.3390/fractalfract5030098
   Web of Science ®Google Scholar
• Thabet, H., & Kendre, S. (2018). Analytical solutions for conformable space-time fractional partial differential equations via fractional differential transform. Chaos, Solitons and Fractals, 109, 238–245. doi:10.1016/j.chaos.2018.03.001
   Web of Science ®Google Scholar