Citation: Mohammed Al-Refai, Dumitru Baleanu. Comparison principles of fractional differential equations with non-local derivative and their applications[J]. AIMS Mathematics, 2020, 6(2): 1443-1451. doi: 10.3934/math.2021088
[1] | A. M. A. El-Sayed, M. Gaber, On the finite Caputo and finite Riesz derivatives, Electron. J. Theor. Phys., 3 (2006), 81-95. |
[2] | A. B. Malinowska, D. F. Torres, Fractional calculus of variations for a combined Caputo derivative, Fract. Calc. Appl. Anal., 14 (2011), 523-537. |
[3] | T. Odzijewics, A. B. Malinowska, D. F. Torres, Fractional variable calculus with classical and combined Caputo derivatives, Nonlinear Anal.: Theory, Method. Appl., 75 (2012), 1507-1515. |
[4] | T. Odzijewics, A. B. Malinowska, D. F. Torres, Fractional calculus of variations in terms of a generalized fractional integral with applications to physics, Abstr. Appl. Anal., 2012 (2012), 1-24. |
[5] | S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional integrals and derivatives: theory and applications, Gordon and Breach, Yverdon, 1993. |
[6] | F. Chen, D. Baleanu, G. C. Wu, Existence results of fractional differential equations with RieszCaputo derivative, Eur. Phys. J. Spec. Top., 226 (2017), 3411-3425. |
[7] | H. Ye, F. Liu, V. Anh, I. Turner, Maximum principle and numerical method for the multi-term time space Riesz-Caputo fractional differential equations, Appl. Math. Comput., 227 (2014), 531-540. |
[8] | M. Al-Refai, Basic results on nonlinear eigenvalue problems of fractional order, Electron. J. Differ. Equ., 2012 (2012), 1-12. |
[9] | M. Al-Refai, Y. Luchko, Maximum principles for the fractional diffusion equations with the Riemann-Liouville fractional derivative and their applications, Fract. Calc. Appl. Anal., 17 (2014), 483-498. |
[10] | M. Al-Refai, Y. Luchko, Analysis of fractional diffusion equations of distributed order: maximum principles and its applications, Analysis, 36 (2016), 123-133. |
[11] | M. Al-Refai, K. Pal, A maximum principle for a fractional boundary value problem with convection term and applications, Math. Model. Anal., 24 (2019), 62-71. |
[12] | M. Al-Refai, On the fractional derivative at extreme points, Elect. J. Qual. Theory Differ. Equ., 2012 (2012), 1-5. |
[13] | Y. Luchko, Maximum principle for the generalized time-fractional diffusion equation, J. Math. Anal. Appl., 351 (2009), 218-223. |