On a problem for the nonlinear diffusion equation with conformable time derivative

References

• Khalil AR, Yousef A, Sababheh M. A new definition of fractional derivative. J Comput Appl Math. 2014;264:65–70.
   Web of Science ®Google Scholar
• Miller KS. An introduction to fractional calculus and fractional differential equations. New York (NY): Wiley and Sons; 1993.
   Google Scholar
• Oldham K, Spanier J. The fractional calculus theory and applications of differentiation and integration of arbitrary order. USA: Academic Press; 1974.
   Google Scholar
• Kilbas A, Srivastava H, Trujillo J. Theory and applications of fractional differential equations. New York (NY): North-Holland; 2006. (Mathematics studies).
   Google Scholar
• Podlubny I. Fractional differential equations. USA: Academic Press; 1999.
   Google Scholar
• Abdeljawad T. On conformable fractional calculus. J Comput Appl Math. 2015;279:57–66.
   Web of Science ®Google Scholar
• Alharbia FM, Baleanu D, Abdelhalim E. Physical properties of the projectile motion using the conformable derivative. Chinese J Phys. 2019;58:18–28.
   Web of Science ®Google Scholar
• Atangana A, Baleanu D, Alsaedi A. New properties of conformable derivative. Open Math. 2015;13:889–898.
   Web of Science ®Google Scholar
• Baleanu D, Jarad F, Uğurlu E. Singular conformable sequential differential equations with distributional potentials. Quaest Math. 2019;42(3):277–287.
   Web of Science ®Google Scholar
• Baleanu D, Fernandez A. On some new properties of fractional derivatives with Mittag–Leffler kernel. Commun Nonlinear Sci Numer Simul. 2018;59:444–462.
   Web of Science ®Google Scholar
• Baleanu D, Mousalou A, Rezapour S. A new method for investigating approximate solutions of some fractional integro-differential equations involving the Caputo–Fabrizio derivative. Adv Differ Equ. 2017;2017:Article number 51, 12 pages.
   Web of Science ®Google Scholar
• Batarfi H, Losada J, Nieto JJ, et al. Three-point boundary value problems for conformable fractional differential equations. J Funct Spaces. 2015;2015:Article ID 706383, 6 pages.
   Web of Science ®Google Scholar
• Çenesiz Y, Baleanu D, Kurt A, et al. New exact solutions of Burgers' type equations with conformable derivative. Waves Random Complex Media. 2017;27(1):103–116.
   Web of Science ®Google Scholar
• Inc M, Yusuf A, Aliyu AI, et al. Soliton structures to some time-fractional nonlinear differential equations with conformable derivative. Opt Quantum Electr. 2017;50(1):Article number: 20.
   Web of Science ®Google Scholar
• Inc M, Yusuf A, Aliyu AI, et al. Dark and singular optical solitons for the conformable space-time nonlinear Schrödinger equation with Kerr and power law nonlinearity. Optik. 2018;162:65–75.
   Web of Science ®Google Scholar
• Yusuf A, Inc M, Aliyu AI, et al. Conservation laws, soliton-like and stability analysis for the time fractional dispersive long-wave equation. Adv Differ Equ. 2018;2018:Article Number 319, 11 pages.
   Web of Science ®Google Scholar
• Jaiswal A, Bahuguna D. Semilinear conformable fractional differential equations in Banach spaces. Differ Equ Dyn Syst. 2019;27(1–3):313–325.
   Web of Science ®Google Scholar
• Li M, Wang JR, O'Regan D. Existence and Ulam's stability for conformable fractional differential equations with constant coefficients. Bull Malaysian Math Sci Soc. 2019;42(4):1791–1812.
   Web of Science ®Google Scholar
• Tariboon J, Ntouyas KS. Oscillation of impulsive conformable fractional differential equations. Open Math. 2016;14:497–508.
   Web of Science ®Google Scholar
• Yang S, Wang L, Zhang S. Conformable derivative: application to non-Darcian flow in low-permeability porous media. Appl Math Lett. 2017;79:105–110.
   Web of Science ®Google Scholar
• Zhong W, Wang L. Basic theory of initial value problems of conformable fractional differential equations. Adv Differ Equ. 2018;2018:Article number 321, 14 pages.
   Web of Science ®Google Scholar
• Wang X, Wang JR, Shen D, et al. Convergence analysis for iterative learning control of conformable fractional differential equations. Math Methods Appl Sci. 2018;41(17):8315–8328.
   Web of Science ®Google Scholar
• Sakamoto K, Yamamoto M. Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems. J Math Anal Appl. 2011;382(1):426–447.
   Web of Science ®Google Scholar
• Bouaouid M, Hilal K, Melliani S. Nonlocal telegraph equation in frame of the conformable time-fractional derivative. Adv Math Phys. 2019;2019:Article ID 7528937.
   Web of Science ®Google Scholar
• Lei G, Cao N, Liu D, et al. A non-linear flow model for porous media based on conformable derivative approach. Energies. 2018;11:1–11.
   Web of Science ®Google Scholar
• Omer AA, Maysaa M, Baleanu D. New exact solution of generalized biological population model. J Nonlinear Sci Appl. 2017;10(7):3916–3929.
   Google Scholar
• Çenesiz Y, Kurt A. The solutions of time and space conformable fractional heat equations with conformable Fourier transform. Acta Univ Sapientiae Math. 2015;7(2):130–140.
   Web of Science ®Google Scholar
• Çenesiz Y, Kurt A, Nane E. Stochastic solutions of conformable fractional Cauchy problems. Stat Probab Lett. 2017;124:126–131.
   Web of Science ®Google Scholar
• Mu J, Ahmad B, Huang S. Existence and regularity of solutions to time-fractional diffusion equations. Comput Math Appl. 2017;73(6):985–996.
   Web of Science ®Google Scholar
• Niu M, Xie B. Regularity of a fractional partial differential equation driven by space-time white noise. Proc Am Math Soc. 2010;138(4):1479–1489.
   Web of Science ®Google Scholar
• Otárola E, Salgado A. Regularity of solutions to space-time fractional wave equations: a PDE approach. Fract Calc Appl Anal. 2018;21(5):1262–1293.
   Web of Science ®Google Scholar
• Evans LC. Partial differential equations. Vol. 19. Providence (RI): American Mathematical Society; 1997.
   Google Scholar
• Tuan NH, Thang LD, Trong DD, et al. Approximation of mild solutions of the linear and nonlinear elliptic equations. Inverse Probl Sci Eng. 2015;23(7):1237–1266.
   Web of Science ®Google Scholar