Existence results for systems of conformable fractional differential equations
Bouharket Bendouma; Alberto Cabada; Ahmed Hammoudi
Archivum Mathematicum (2019)
- Volume: 055, Issue: 2, page 69-82
- ISSN: 0044-8753
Access Full Article
topAbstract
topHow to cite
topReferences
top- Abdeljawad, T., 10.1016/j.cam.2014.10.016, J. Comput. Appl. Math. 279 (2015), 57–66. (2015) MR3293309DOI10.1016/j.cam.2014.10.016
- Abdeljawad, T., AlHorani, M., Khalil, R., Conformable fractional semigroups of operators, J. Semigroup Theory Appl. 2015 (2015), 9 pages. (2015)
- Anderson, D.R., Avery, R.I., Fractional-order boundary value problem with Sturm-Liouville boundary conditions, Electronic J. Differential Equ. 2015 (29) (2015), 10 pages. (2015) MR3335759
- Batarfi, H., Losada, J., Nieto, J.J., Shammakh, W., Three-point boundary value problems for conformable fractional differential equations, J. Function Spaces 2015 (2015), 6 pages. (2015) MR3326681
- Bayour, B., Torres, D.F.M., 10.1016/j.cam.2016.01.014, J. Comput. Appl. Math. 312 (2016), 127–133. (2016) MR3557866DOI10.1016/j.cam.2016.01.014
- Benchohra, M., Cabada, A., Seba, D., An existence result for nonlinear fractional differential equations on Banach spaces, Boundary Value Problem 2009 (2009), 11 pages. (2009) MR2525581
- Bendouma, B., Cabada, A., Hammoudi, A., Existence of solutions for conformable fractional problems with nonlinear functional boundary conditions, submitted.
- Benkhettou, N., Hassani, S., Torres, D.F.M., 10.1016/j.jksus.2015.05.003, J. King Saud Univ. Sci. 28 (1) (2016), 93–98. (2016) DOI10.1016/j.jksus.2015.05.003
- Cabada, A., Green’s Functions in the Theory of Ordinary Differential Equations, Springer, New York, 2014. (2014) MR3155625
- Cabada, A., Hamdi, Z., 10.1016/j.amc.2013.11.057, Appl. Appl. Math. Comput. 228 (2014), 251–257. (2014) MR3151912DOI10.1016/j.amc.2013.11.057
- Cabada, A., Hamdi, Z., 10.1515/gmj-2016-0086, Georgian Math. J. 24 (1) (2017), 41–53. (2017) MR3607239DOI10.1515/gmj-2016-0086
- Cabada, A., Wang, G., 10.1016/j.jmaa.2011.11.065, J. Math. Anal. Appl. 389 (1) (2012), 403–411. (2012) MR2876506DOI10.1016/j.jmaa.2011.11.065
- Chung, W.S., 10.1016/j.cam.2015.04.049, J. Comput. Appl. Math. 290 (2015), 150–158. (2015) MR3370399DOI10.1016/j.cam.2015.04.049
- Frigon, M., O’Regan, D., Existence results for initial value problems in Banach spaces, Differ. Equ. Dyn. Syst. 2 (1994), 41–48. (1994) MR1386037
- Frigon, M., O’Regan, D., 10.1016/S0893-9659(97)00057-8, Appl. Math. Lett. 10 (1997), 41–46. (1997) MR1458151DOI10.1016/S0893-9659(97)00057-8
- Gilbert, H., Existence theorems for first order equations on time scales with Carathédory functions, Adv. Difference Equ. 2010 (2010), 20 pages, Article ID 650827. (2010) MR2747083
- Gökdoǧan, A., Ünal, E., Çelik, E., Existence and uniqueness theorems for sequential linear conformable fractional differential equations, arXiv preprint, 2015. MR3527883
- Gözütok, N.Y., Gözütok, U., Multivariable conformable fractional calculus, math.CA 2017.
- Gulsen, T., Yilmaz, E., Goktas, S., Conformable fractional Dirac system on time scales, J. Inequ. Appl. 2017 (2017), 1–10. (2017) MR3669797
- Iyiola, O.S., Nwaeze, E.R., 10.18576/pfda/020204, Progr. Fract. Differ. Appl. 2 (2) (2016), 115–122. (2016) DOI10.18576/pfda/020204
- Katugampola, U.N., A new fractional derivative with classical properties, preprint, 2014. MR3298307
- Khaldi, R., Guezane-Lakoud, A., 10.18576/pfda/030407, Progr. Fract. Differ. Appl. 3 (4) (2017), 323–329. (2017) DOI10.18576/pfda/030407
- Khalil, R., Horani, M. Al, Yousef, A., Sababheh, M., 10.1016/j.cam.2014.01.002, J. Comput. Appl. Math. 264 (2014), 65–70. (2014) MR3164103DOI10.1016/j.cam.2014.01.002
- Kilbas, A., Srivastava, M.H., Trujillo, J.J., Theory and Application of Fractional Differential Equations, vol. 204, North Holland Mathematics Studies, 2006. (2006) MR2218073
- Magin, R.L., 10.1615/CritRevBiomedEng.v32.10, CR in Biomedical Engineering 32 (1) (2004), 1–104. (2004) DOI10.1615/CritRevBiomedEng.v32.10
- Mirandette, B., Résultats d’existence pour des systèmes d’équations différentielles du premier ordre avec tube-solution, Mémoire de matrise, Université de Montréal, 1996. (1996)
- Nwaeze, E.R., 10.18576/pfda/020406, Progr. Fract. Differ. Appl. 2 (4) (2016), 287–291. (2016) DOI10.18576/pfda/020406
- Ortigueira, M.D., Machado, J.A. Tenreiro, 10.1016/j.jcp.2014.07.019, J. Comput. Phys. 293 (2015), 4–13. (2015) MR3342452DOI10.1016/j.jcp.2014.07.019
- Pospisil, M., Skripkova, L.P., Sturm’s theorems for conformable fractional differential equations, Math. Commun. 21 (2016), 273–281. (2016) MR3517494
- Shi, A., Zhang, S., Upper and lower solutions method and a fractional differential equation boundary value problem, Progr. Fract. Differ. Appl. 30 (2009), 13 pages. (2009) MR2506151
- Shugui, K., Huiqing, C., Yaqing, Y., Ying, G., Existence and uniqueness of the solutions for the fractional initial value problem, Electr. J. Shanghai Normal University (Natural Sciences) 45 (3) (2016), 313–319. (2016)
- Wang, Y., Zhou, J., Li, Y., Fractional Sobolev’s spaces on time scales via conformable fractional calculus and their application to a fractional differential equation on time scales, Adv. Math. Phys. 2016 (2016), 21 pages. (2016) MR3579208
- Yang, X.J., Baleanu, D., Machado, J.A.T., Application of the local fractional Fourier series to fractal signals, Discontinuity and complexity in nonlinear physical systems, Springer, Cham, 2014, pp. 63–89. (2014) MR3204525
- Zhang, S., Su, X., 10.1016/j.camwa.2011.03.008, Comput. Math. Appl. 62 (3) (2011), 1269–1274. (2011) MR2824713DOI10.1016/j.camwa.2011.03.008