×

Extremal mild solutions to Hilfer evolution equations with non-instantaneous impulses and nonlocal conditions. (English) Zbl 1522.34086


MSC:

34G20 Nonlinear differential equations in abstract spaces
34K37 Functional-differential equations with fractional derivatives
47N20 Applications of operator theory to differential and integral equations
Full Text: DOI

References:

[1] Agarwal, R.; Almeida, R.; Hristova, S.; O’Regan, D., Non-instantaneous impulsive fractional differential equations with state dependent delay and practical stability, Acta Mathematica Scientia, 41B, 5, 1699-1718 (2021) · Zbl 1513.34294 · doi:10.1007/s10473-021-0518-1
[2] Amann, H., Parabolic evolution equations and nonlinear eigenvalue problem in ordered Banach spaces, SIAM Rev., 18, 4, 620-709 (1976) · Zbl 0345.47044 · doi:10.1137/1018114
[3] Abada, N.; Benchohra, M.; Hammouche, H., Existence and controllability results for nondensely defined impulsive semilinear functional differential inclusions, J. Differential Equ., 246, 3834-3863 (2009) · Zbl 1171.34052 · doi:10.1016/j.jde.2009.03.004
[4] Abbas, S.; Benchohra, M., Uniqueness and Ulam stabilities results for partial fractional differential equations with not instantaneous impulses, Appl. Math. Comput., 257, 190-198 (2015) · Zbl 1338.35455
[5] Alsheekhhussain, Z., Wang, J. R., Ibrahim, A., G.: Asymptotically periodic behavior of solutions to fractional non-instantaneous impulsive semilinear differential inclusions with sectorial operator. Advances in Difference Equations 2021(330), (2021) · Zbl 1494.34172
[6] Brill, H., A semilinear Sobolev evolution equation in Banach space, Journal of Differential Equations, 24, 421-425 (1977) · Zbl 0346.34046 · doi:10.1016/0022-0396(77)90009-2
[7] Banas̀, J., Goebel, K.: Measures of Noncompactness in Banach Spaces. In Lecture Notes in Pure and Applied Mathematics. Marcel Dekker, New York (1980) · Zbl 0441.47056
[8] Borah, J.; Bora, SN, Existence of mild solution of a class of nonlinear fractional order differential equations with not instantaneous impulses, Fract. Calc. Appl. Anal., 22, 2, 495-508 (2019) · Zbl 1428.34114 · doi:10.1515/fca-2019-0029
[9] Batista, M. R., Da Mota, J. C.: Monotone iterative method of upper and lower solutions applied to a multilayer combustion model in porous media. Nonlinear Anal. Real World Appl. 58, 103223 (2021). https://www.sciencedirect.com/science/article/abs/pii/S1468121820301413 · Zbl 1454.80009
[10] Colao, V.; Mugliam, L.; Xu, H., Existence of solutions for a second-order differential equation with non-instantaneous impulses and delay, Annali di Matematica., 195, 697-716 (2016) · Zbl 1344.34084 · doi:10.1007/s10231-015-0484-0
[11] Chaudhary, R.; Reich, S., Extremal mild solutions to fractional delay integro-differential equations with non-instantaneous impulses, Appl. Anal. (2021) · Zbl 1512.34139 · doi:10.1080/00036811.2021.2011245
[12] Chen, P.; Zhang, X.; Li, Y., Existence of mild solutions to partial differential equations with non-instantaneous impulses, Electron. J. Differ. Equ., 241, 1-11 (2016) · Zbl 1350.34047
[13] Chen, P.; Zhang, X.; Li, Y., Non-autonomous evolution equations of parabolic type with non-non-instantaneous impulses, Mediterr. J. Math., 16, 118 (2019) · Zbl 1483.35333 · doi:10.1007/s00009-019-1384-0
[14] Chen, P.; Zhang, X.; Li, Y., Non-autonomous parabolic evolution equations with non-instantaneous impulses governed by noncompact evolution families, J. Fixed Point Theory and Appl., 21, 84 (2019) · Zbl 1423.35425 · doi:10.1007/s11784-019-0719-6
[15] Chen, P.; Zhang, X.; Li, Y., Iterative method for a new class of evolution equations with non-instantaneous impulses, Taiwanese Journal of Mathematics, 21, 4, 913-942 (2017) · Zbl 1390.34189 · doi:10.11650/tjm/7912
[16] Du, Y., Fixed point of increasing operators in ordered Banach spaces and applications, Appl. Anal., 38, 1-2, 1-20 (1990) · Zbl 0671.47054 · doi:10.1080/00036819008839957
[17] Du, SW; Lakshmikantham, V., Monotone iterative technique for differential equations in a Banach space, J. Math. Anal. Anal., 87, 2, 454-459 (1982) · Zbl 0523.34057 · doi:10.1016/0022-247X(82)90134-2
[18] Deimling, K., Nonlinear Functional Analysis (1985), New York: Springer-Verlag, New York · Zbl 0559.47040 · doi:10.1007/978-3-662-00547-7
[19] Furati, K.M., Kassim, M.D., Tatar,N.e-.: Existence and uniqueness for a problem involving Hilfer factional derivative. Comput. Math. Appl. 64, 1612-1626 (2012) · Zbl 1268.34013
[20] Guo, D.; Liu, X., Extremal solutions of nonlinear impulsive integrodifferential equations in Banach spaces, J. Math. Anal. Anal., 177, 2, 538-552 (1982) · Zbl 0787.45008 · doi:10.1006/jmaa.1993.1276
[21] Guo, D.; Lakshmikantham, V., Nonlinear Problem in Abstract Cone (1988), Boston, MA: Notes and Resports in Mathematics in Science and Engineering. Academic Press, Boston, MA · Zbl 0661.47045
[22] Gu, H.; Trujillo, JJ, Existence of mild solution for evolution equation with Hilfre fractional derivative, Applied Mathematics and Computation, 257, 344-354 (2015) · Zbl 1338.34014 · doi:10.1016/j.amc.2014.10.083
[23] Gou, H., Li, B.: Study on Sobolev type Hilfer fractional integro-differential equations with delay. J. Fixed Point Theory Appl. 20(1), (2018) · Zbl 1454.34107
[24] Gou H.: Monotone iterative technique for Hilfer fractional evolution equations with nonlocal conditions. Bull Sci Math. 167, 102946 (2021). https://www.sciencedirect.com/science/article/abs/pii/S0007449721000026 · Zbl 1464.34102
[25] Gautam, GR; Dabas, J., Mild solutions for a class of neutral fractional functional differential equations with not instantaneous impulses, Appl. Math. Comput., 259, 480-489 (2015) · Zbl 1390.34221
[26] Hilfer, R., Applications of Fractional Caiculus in Physics (2000), Singapore: World Scientific, Singapore · Zbl 0998.26002 · doi:10.1142/3779
[27] Hilfer, R., Luchko, Y., Tomovski, Z̆.: Operational method for the solution of fractional differential equations with generalized Riemann-Liouville fractional derivatives. Fract. Calc. Appl. Anal. 12(3), 299-318 (2009) · Zbl 1182.26011
[28] Heinz, HP, On the behaviour of measure of noncompactness with respect to differentiation and integration of vector-valued functions, Nonlinear Anal., 7, 1351-1371 (1983) · Zbl 0528.47046 · doi:10.1016/0362-546X(83)90006-8
[29] Hernández, E.; O’Regan, D., On a new class of abstract impulsive differential equations, Proc. Amer. Math. Soc., 141, 1641-1649 (2013) · Zbl 1266.34101 · doi:10.1090/S0002-9939-2012-11613-2
[30] Lakshmikantham, V., Bainov, D.D., Simeonov, P.S.: Theory of Impulsive Differential Equations, Series in Modern Applied Mathematics 6. World Scientific, Teaneck, NJ (1989) · Zbl 0719.34002
[31] Li, Y.; Liu, Z., Monotone iterative technique for addressing impulsive integro differential equations in Banach spaces, Nonlinear Anal., 66, 1, 83-92 (2007) · Zbl 1109.34005 · doi:10.1016/j.na.2005.11.013
[32] Li, F.; Liang, J.; Xu, HK, Existence of mild solutions for fractioanl integrodifferential equations of Sobolev type with nonlocal conditions, Journal of Mathematical Analysis and Applications, 391, 510-525 (2012) · Zbl 1242.45009 · doi:10.1016/j.jmaa.2012.02.057
[33] Li, Y., Existence of solutions of initial value problems for abstract semilinear evolution equations, Acta Math. Sin., 48, 1089-1094 (2005) · Zbl 1124.34341
[34] Liu, K., Fec̆kan, M., O’Regan, D.: \((\omega ,c)\)-periodic solutions for time-varying non-instantaneous impulsive differential systems. Appl. Anal. 2021. doi:10.1080/00036811.2021.1895123 · Zbl 1509.34019
[35] Liu, L., Iterative method for solutions and coupled quasi-solutions of nonlinear integro-differential equations of mixed type in Banach spaces, Nonlinear Analysis, 42, 583-598 (2000) · Zbl 0962.45007 · doi:10.1016/S0362-546X(99)00116-9
[36] Meraj, A., Pandey, D.N.: Existence of mild solutions for fractional non-instantaneous impulsive integral differential equations with nonlocal conditions. Arab Journal Mathematical Sciences 26(1), (2018). DOI:doi:10.1016/j.ajmsc.2018.11.002 · Zbl 1488.34405
[37] Ngo, VH; O’Regan, D., A remark on \(\psi \)-Hilfer fractional differential equations with non-instantaneous impulses, Math. Meth. Appl. Sci., 2020, 1-15 (2020) · Zbl 1451.34012
[38] Pazy, A., Semigroups of Linear Operators and Applications to Partial Differential Equations (1983), Berlin: Springer-Verlag, Berlin · Zbl 0516.47023 · doi:10.1007/978-1-4612-5561-1
[39] Pierri, M.; O’Regan, D.; Rolnik, V., Existence of solutions for semi-linear abstract differential equations with not instantaneous impulses, Appl. Math. Comput., 219, 6743-6749 (2013) · Zbl 1293.34019
[40] Raghavan, D.; Nagarajan, S., Extremal mild solutions of fractional evolution equation with mixed monotone impulsive conditions, Bull. Malays. Sci. Sci. Soc., 45, 1427-1452 (2022) · Zbl 1501.34013
[41] da Vanterler, C.; Sousa, J.; Jarad, F.; Abdeljawad, ET, Existence of mild solutions to Hilfer (fractional evolution eqaitions in Banach space, Annals of Functional Analysis, 12, 1-16 (2021) · Zbl 1458.34032 · doi:10.1007/s43034-020-00095-5
[42] Wang, J.; Zhou, Y.; Lin, Z., On a new class of impulsive fractional differential equations, Appl. Math. Comput., 242, 649-657 (2014) · Zbl 1334.34022
[43] Yu, X.; Wang, J., Periodic boundary value problems for nonlinear impulsive evolution equations on Banach spaces, Commun. Nonlinear Sci. Numer. Simul., 22, 980-989 (2015) · Zbl 1339.34069 · doi:10.1016/j.cnsns.2014.10.010
[44] Zhang, X.; Li, Y.; Chen, P., Existence of extremal mild solutions for the initial value problem of evolution equations with non-instantaneous impulses, J. Fixed Point Theory and Appl., 19, 3013-3027 (2017) · Zbl 1386.34112 · doi:10.1007/s11784-017-0467-4
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.