[1] Bateman H. Some recent researches on the motion of fluids. Monthly Weather Review, 1915, 43(4):163-170 [2] Cole J D. On a quasi-linear parabolic equation occurring in aerodynamics. Quarterly of Applied Mathematics, 1951, 9(3):225-236 [3] Benton E R, George W P. A table of solutions of the one-dimensional Burgers equation. Quart Appl Math, 1972, 30(2):195-212 [4] Katatbeh Q D, Fethi Bin M B. Applications of the Sumudu transform to fractional differential equations. Nonlinear Studies, 2011, 18(1):99-112 [5] Kumar D, Singh J, Kılıçman A. An efficient approach for fractional Harry Dym equation by using Sumudu transform. Abstract and Applied Analysis, 2013, 2013:608943 [6] Anderson D R, Darin J U. Newly defined conformable derivatives. Adv Dyn Syst Appl, 2015, 10(2):109-137 [7] Jarad F, Uğurlu E, Abdeljawad T, Baleanu D. On a new class of fractional operators. Advances in Difference Equations, 2017, 2017(1):247 [8] Jarad F, Abdeljawad T, Alzabut J. Generalized fractional derivatives generated by a class of local proportional derivatives. The European Physical Journal Special Topics, 2017, 226(16):3457-3471 [9] Abdeljawad T, Al-Mdallal Q M, Hajji M A. Arbitrary order fractional difference operators with discrete exponential kernels and applications. Discrete Dynamics in Nature and Society, 2017, 2017:4149320 [10] Mohammed P O, Hamasalh F K. New conformable fractional integral inequalities of Hermite-Hadamard type for convex functions. Symmetry, 2019, 11(2):263 [11] Jarad F, Bayram K, Abdeljawad T, Baleanu D. On the discrete sumudu transform. Romanian Reports in Physics, 2012, 64(2):347-356 [12] Al-Refai M, Abdeljawad T. Fundamental results of conformable Sturm-Liouville eigenvalue problems. Complexity, 2017, 2017:Art 3720471 [13] Kumar S, Kumar R, Cattani C, Samet B. Chaotic behaviour of fractional predator-prey dynamical system. Chaos, Solitons & Fractals, 2020, 135:109811 [14] Kumar S, Kumar R, Agarwal R P, Samet B. A study of fractional Lotka-Volterra population model using Haar wavelet and Adams-Bashforth-Moulton methods. Math Methods Appl Sci, 2020, 43(8):5564-5578 [15] Kumar S, Kumar A, Samet B, Gómez-Aguilar J F, Osman M S. A chaos study of tumor and effector cells in fractional tumor-immune model for cancer treatment. Chaos, Solitons & Fractals, 2020, 141:110321 [16] Ghanbari B, Kumar S, Kumar R. A study of behaviour for immune and tumor cells in immunogenetic tumour model with non-singular fractional derivative. Chaos, Solitons & Fractals, 2020, 133:109619 [17] Kumar S, Kumar A, Samet B, Dutta H. A study on fractional host-parasitoid population dynamical model to describe insect species. Numerical Methods for Partial Differential Equations, 2021, 37(2):1673-1692 [18] Kumar S, Ghosh S, Samet B, Goufo E F D. An analysis for heat equations arises in diffusion process using new Yang-Abdel-Aty-Cattani fractional operator. Math Methods Appl Sci, 2020, 43(9):6062-6080 [19] Kumar S. A new analytical modelling for fractional telegraph equation via Laplace transform. Appl Math Modell, 2014, 38(13):3154-3163 [20] Kumar S, Nisar K S, Kumar R, Cattani C, Samet B. A new Rabotnov fractional-exponential functionbased fractional derivative for diffusion equation under external force. Math Methods Appl Sci, 2020, 43(7):4460-4471 [21] Kumar S, Rashidi M M. New analytical method for gas dynamics equation arising in shock fronts. Comput Phys Commun, 2014, 185(7):1947-1954 [22] Eltayeb H, Bachar I, Kılıçman A. On conformable double laplace transform and one dimensional fractional coupled Burgers' equation. Symmetry, 2019, 11(3):417 [23] Çenesiz Y, Baleanu D, Kurt A, Tasbozan O. New exact solutions of Burgers' type equations with conformable derivative. Waves in Random and Complex Media, 2017, 27(1):103-116 [24] Liu J, Hou G. Numerical solutions of the space-and time-fractional coupled Burgers equations by generalized differential transform method. Appl Math Comput, 2011, 217(16):7001-7008 [25] Abdeljawad T. On conformable fractional calculus. J Comput Appl Math, 2015, 279:57-66 [26] Silva F S, Moreira D M, Moret M A. Conformable Laplace transform of fractional differential equations. Axioms, 2018, 7(3):55 [27] Özkan O, Kurt A. On conformable double Laplace transform. Optical and Quantum Electronics, 2018, 50(2):1-9 [28] Çenesiz Y, Baleanu D, Kurt A, Tasbozan O. New exact solutions of Burgers' type equations with conformable derivative. Waves in Random and Complex Media, 2017, 27(1):103-116 [29] Katugampola U N. A new fractional derivative with classical properties. arXiv:1410.6535, 2014 [30] Khalil R, Al Horani M, Yousef A, Sababheh M. A new definition of fractional derivative. J Comput Appl Math, 2014, 264:65-70 [31] Thabet H, Kendre S. Analytical solutions for conformable space-time fractional partial differential equations via fractional differential transform. Chaos, Solitons & Fractals, 2018, 109:238-245 [32] Eslami M. Exact traveling wave solutions to the fractional coupled nonlinear Schrodinger equations. Appl Math Comput, 2016, 285:141-148 [33] Abdeljawad T, Al Horani M, Khalil R. Conformable fractional semigroups of operators. J Semigroup Theory Appl, 2015, 2015:Article-ID [34] Eltayeb H, Mesloub S, Kılıçman A. A note on a singular coupled Burgers equation and double Laplace transform method. J Nonlinear Sci Appl, 2018, 11:635-643 |