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Existence of solution for a conformable fractional Cauchy problem with nonlocal condition. (English) Zbl 1505.34118

MSC:

34K37 Functional-differential equations with fractional derivatives
34K10 Boundary value problems for functional-differential equations
34K30 Functional-differential equations in abstract spaces
47N20 Applications of operator theory to differential and integral equations
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[1] Ezzinbi, K.; Liu, J. H., defined evolution equation with nonlocal conditions, Mathematical and Computer Modelling, 36, 1027-1038 (2002) · Zbl 1035.34063 · doi:10.1016/S0895-7177(02)00256-X
[2] Pazy, A., Semigroups of linear operators and applications to partial diffrential equations, Applied Mathematical Sciences, 44 (1983), Springer, New York, NY, USA · Zbl 0516.47023
[3] Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J., Theory and Applications of Fractional Differential Equations (2006), Amesterdam, Netherlands: Elsevier, Amesterdam, Netherlands · Zbl 1092.45003
[4] Miller, K. S., An Introduction to Fractional Calculus and Fractional Differential Equations (1993), New York, NY, USA: Wiley and Sons, New York, NY, USA · Zbl 0789.26002
[5] Ezzinbi, K.; Fu, X.; Hilal, K., Existence and regularity in the -norm for some neutral partial differential equations with nonlocal conditions, Nonlinear Analysis, 67, 5, 1613-1622 (2007) · Zbl 1119.35105 · doi:10.1016/j.na.2006.08.003
[6] Bouaouid, M.; Hilal, K.; Melliani, S., Sequential evolution conformable differential equations of second order with nonlocal condition, Advances in Difference Equations, 2019, 1, 21 (2019) · Zbl 1458.34014 · doi:10.1186/s13662-019-1954-2
[7] Khalil, R.; Al Horani, M.; Yousef, A.; Sababheh, M., A new definition of fractional derivative, Journal of Computational and Applied Mathematics, 264, 65-70 (2014) · Zbl 1297.26013 · doi:10.1016/j.cam.2014.01.002
[8] Samko, S. G.; Kilbas, A. A.; Marichev, O. I., Fractional Integrals and Derivatives 7eory and Applications (1993), Amsterdam, Netherlands: Gordon Breach Science Publishers, Amsterdam, Netherlands · Zbl 0818.26003
[9] Abdeljawad, T., On conformable fractional calculus, Journal of Computational and Applied Mathematics, 279, 57-66 (2015) · Zbl 1304.26004 · doi:10.1016/j.cam.2014.10.016
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