Asymptotical stability analysis of conformable fractional systems

References

• Bahaa GM, Hamiaz A. Optimal control problem for coupled time-fractional diffusion systems with final observations. J Taibah Univ Sci. 2019;13(1):124–135. doi: 10.1080/16583655.2018.1545560
   Web of Science ®Google Scholar
• Khamessi B, Hamiaz A. Existence and exact asymptotic behaviour of positive solutions for fractional boundary value problem with P-Laplacian operator. J Taibah Univ Sci. 2019;13(1):370–376. doi: 10.1080/16583655.2019.1579953
   Web of Science ®Google Scholar
• Bohner M, Hatipoǧlu VF. Cobweb model with conformable fractional derivatives. Math Methods Appl Sci. 2018;41(18):9010–9017. doi: 10.1002/mma.4846
   Web of Science ®Google Scholar
• Acan O, Qurashi MMA, Baleanu D. New exact solution of generalized biological population model. J Nonlinear Sci Appl. 2017;10(7):3916–3929. doi: 10.22436/jnsa.010.07.44
   Google Scholar
• Hatipoǧlu VF, Alkan S, Secer A. An efficient scheme for solving a system of fractional differential equations with boundary conditions. Adv Differ Equ. 2017;204:1–13.
   Google Scholar
• Kurt A. New periodic wave solutions of a time fractional integrable shallow water equation. Appl Ocean Res. 2019;85:128–135. doi: 10.1016/j.apor.2019.01.029
   Web of Science ®Google Scholar
• Tasbozan O, Kurt A, Tozar A. New optical solutions of complex Ginzburg-Landau equation arising in semiconductor lasers. Appl Phys B. 2019;125:6–104. doi: 10.1007/s00340-019-7217-9
   Web of Science ®Google Scholar
• Bayram M, Hatipoglu VF, Alkan S, et al. A solution method for integro-differential equations of conformable fractional derivative. Therm Sci. 2018;22(1):7–14. doi: 10.2298/TSCI170624266B
   Google Scholar
• Khalil R, Al Horani M, Yousef A, et al. A new definition of fractional derivative. J Comput Appl Math. 2014;264:65–70. doi: 10.1016/j.cam.2014.01.002
   Web of Science ®Google Scholar
• Ünal E, Gökdoǧan A. Solution of conformable fractional ordinary differential equations via differential transform method. Optik. 2017;128:264–273. doi: 10.1016/j.ijleo.2016.10.031
   Web of Science ®Google Scholar
• Khan TU, Khan MA. Generalized conformable fractional operators. J Comput Appl Math. 2019;346:378–389. doi: 10.1016/j.cam.2018.07.018
   Web of Science ®Google Scholar
• 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. doi: 10.1016/j.chaos.2018.03.001
   Web of Science ®Google Scholar
• Rosales JJ, Godnez FA, Banda V, et al. Analysis of the Drude model in view of the conformable derivative. Optik. 2019;178:1010–1015. doi: 10.1016/j.ijleo.2018.10.079
   Web of Science ®Google Scholar
• Chen C, Jiang YL. Simplest equation method for some time-fractional partial differential equations with conformable derivative. Comput Math Appl. 2018;75:2978–2988. doi: 10.1016/j.camwa.2018.01.025
   Web of Science ®Google Scholar
• Rezazadeh H, Mirhosseini-Alizamini SM, Eslami M, et al. New optical solitons of nonlinear conformable fractional Schrpodinger-Hirota equation. Optik. 2018;172:545–553. doi: 10.1016/j.ijleo.2018.06.111
   Web of Science ®Google Scholar
• Tariboon J, Ntouyas SK. Oscillation of impulsive conformable fractional differential equations. Open Math. 2016;14:497–508. doi: 10.1515/math-2016-0044
   Web of Science ®Google Scholar
• Zhao DZ, Luo MK. General conformable fractional derivative and its physical interpretation. Calcolo. 2017;53:903–917. doi: 10.1007/s10092-017-0213-8
   Google Scholar
• Chung WS, Zare S, Hassanabadi H. Investigation of conformable fractional schrodinger equation in presence of killingbeck and hyperbolic potentials. Commun Theor Phys. 2017;67:250–254. doi: 10.1088/0253-6102/67/3/250
   Web of Science ®Google Scholar
• Liu S, Jiang W, Li XY, et al. Lyapunov stability analysis of fractional nonlinear systems. Appl Math Lett. 2016;51:13–19. doi: 10.1016/j.aml.2015.06.018
   Web of Science ®Google Scholar
• Wang XH, Peng YH, Lu WC. Lyapunov-type inequalities for certain higher order fractional differential equations. J Nonlinear Sci Appl. 2017;10:5064–5071. doi: 10.22436/jnsa.010.09.42
   Google Scholar
• Kayar Z. Lyapunov type inequalities and their applications for quasilinear impulsive systems. J Taibah Univ Sci. 2019;13(1):711–721. doi: 10.1080/16583655.2019.1625188
   Web of Science ®Google Scholar
• Shah K, Ali A, Khan RA. Degree theory and existence of positive solutions to coupled systems of multi-point boundary value problems. Bound Value Probl. 2016;43:1–12.
   Google Scholar
• Alfishawi T. On conformable fractional calculus. J Comput Appl Math. 2015;279:57–66. doi: 10.1016/j.cam.2014.10.016
   Web of Science ®Google Scholar
• Hashemi MS. Invariant subspaces admitted by fractional differential equations with conformable derivatives. Chaos Solitons Fract. 2018;107:161–169. doi: 10.1016/j.chaos.2018.01.002
   Web of Science ®Google Scholar
• Rezazadeh H, Tariq H, Eslami M, et al. New exact solutions of nonlinear conformable time-fractional Phi-4 equation. Chin J Phys. 2018;56:2805–2816. doi: 10.1016/j.cjph.2018.08.001
   Web of Science ®Google Scholar
• Ilie M, Biazar J, Ayati Z. The first integral method for solving some conformable fractional differential equations. Opt Quantum Electron. 2018;50:55. doi: 10.1007/s11082-017-1307-x
   Web of Science ®Google Scholar
• Kumar D, Seadawy AR, Joardar AK. Modified Kudryashov method via new exact solutions for some conformable fractional differential equations arising in mathematical biology. Chin J Phys. 2018;56:75–85. doi: 10.1016/j.cjph.2017.11.020
   Web of Science ®Google Scholar
• Özkan O, Kurt A. The analytical solutions for conformable integral equations and integro-differential equations by conformable Laplace transform. Opt Quantum Electron. 2018;50:81. doi: 10.1007/s11082-018-1342-2
   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. doi: 10.1016/j.spl.2017.01.012
   Web of Science ®Google Scholar
• Yaslan HÇ. Numerical solution of the conformable space-time fractional wave equation. Chin J Phys. 2018;56:2916–2925. doi: 10.1016/j.cjph.2018.09.026
   Web of Science ®Google Scholar
• Bohner M, Hatipoǧlu VF. Dynamic cobweb models with conformable fractional derivatives. Nonlinear Anal Hybrid Syst. 2019;32:157–167. doi: 10.1016/j.nahs.2018.09.004
   Web of Science ®Google Scholar
• Osman M, Korkmaz A, Rezazadeh H, et al. The unified method for conformable time fractional schro¨dinger equation with perturbation terms. Chin J Phys. 2018;56:2500–2506. doi: 10.1016/j.cjph.2018.06.009
   Google Scholar
• Foroutan M, Kumar D, Manafian J, et al. New explicit soliton and other solutions for the conformable fractional biswas-milovic equation with kerr and parabolic nonlinearity through an integration scheme. Optik. 2018;170:190–202. doi: 10.1016/j.ijleo.2018.05.129
   Web of Science ®Google Scholar
• Chen LP. Stability and synchronization control of fractional-order nonlinear systems. Chongqing: Chongqing University; 2013.
   Google Scholar
• Wang XH. Mittag-Leffler stabilization of fractional-order nonlinear systems with unknown control coefficients. Adv Differ Equ. 2018;16:1–14.
   Google Scholar
• Liu TD, Wang F, Lu WC, et al. Global stabilization for a class of nonlinear fractional-order systems. Int J Model Simul Sci Comput. 2019;10:1941009.
   Google Scholar
• Souahi A, Ben Makhlouf A, Hammami MA. Stability analysis of conformable fractional-order nonlinear systems. Indagationes Math. 2017;28:1265–1274. doi: 10.1016/j.indag.2017.09.009
   Web of Science ®Google Scholar