المؤلفون: Benchohra, Mouffak, Bouriah, Soufyane, Lazreg, Jamal E., Nieto, Juan J.

مصطلحات موضوعية: keyword:Hadamard’s fractional derivative, keyword:implicit fractional differential equations in Banach space, keyword:fractional integral, keyword:existence, keyword:Gronwall’s lemma for singular kernels, keyword:Measure of noncompactness, keyword:fixed point, msc:26A33, msc:34A08

وصف الملف: application/pdf

Relation: mr:MR3674595; zbl:Zbl 1362.34010; reference:[1] Abbas, S., Benchohra, M., N’Guérékata, G. M.: Topics in Fractional Differential Equations. Springer-Verlag, New York, 2012. Zbl 1273.35001, MR 2962045; reference:[2] Abbas, S., Benchohra, M., N’Guérékata, G. M.: Advanced Fractional Differential and Integral Equations. Nova Science Publishers, New York, 2015. Zbl 1314.34002, MR 3309582; reference:[3] Agarwal, R. P., Meehan, M., O’Regan, D.: Fixed Point Theory and Applications. Cambridge University Press, Cambridge, 2001. Zbl 0960.54027, MR 1825411, 10.1017/CBO9780511543005.008; reference:[4] Ahmad, B., Ntouyas, S. K.: A fully Hadamard type integral boundary value problem of a coupled system of fractional differential equations. Fract. Calc. Appl. Anal. 17 (2014), 348–360. Zbl 1312.34005, MR 3181059, 10.2478/s13540-014-0173-5; reference:[5] Ahmad, B., Ntouyas, S. K.: Initial value problems of fractional order Hadamard-type functional differential equations. Electron. J. Differential Equations 2015, 77 (2015), 1–9. Zbl 1320.34109, MR 3337854; reference:[6] Akhmerov, K. K., Kamenskii, M. I., Potapov, A. S., Rodkina, A. E., Sadovskii, B. N.: Measures of Noncompactness and Condensing Operators. Birkhäuser Verlag, Basel, Boston, Berlin, 1992. MR 1153247; reference:[7] Appell, J.: Implicit functions, nonlinear integral equations, and the measure of noncompactness of the superposition operator. J. Math. Anal. Appl. 83 (1981), 251–263. Zbl 0495.45007, MR 0632341, 10.1016/0022-247X(81)90261-4; reference:[8] Baleanu, D., Güvenç, Z. B., Machado, J. A. T.: New Trends in Nanotechnologiy and Fractional Calculus Applications. Springer, New York, 2010. MR 2605606; reference:[9] Banaś, J., Goebel, K.: Measures of Noncompactness in Banach Spaces. Lecture Notes in Pure and Applied Mathematics 60, Marcel Dekker, New York, 1980. MR 0591679; reference:[10] Banaś, J., Olszowy, L.: Measures of noncompactness related to monotonicity. Comment. Math. 41 (2001), 13–23. Zbl 0999.47041, MR 1876707; reference:[11] Benchohra, M., Bouriah, S.: Existence and stability results for nonlinear boundary value problem for implicit differential equations of fractional order.; reference:[12] Benchohra, M., Bouriah, S., Henderson, J.: Existence and stability results for nonlinear implicit neutral fractional differential equations with finite delay and impulses. Comm. Appl. Nonlin. Anal. 22 (2015), 46–67. Zbl 1358.34088, MR 3363687; reference:[13] Butzer, P. L., Kilbas, A. A., Trujillo, J. J.: Compositions of Hadamard-type fractional integration operators and the semigroup property. J. Math. Anal. Appl. 269 (2002), 387–400. Zbl 1027.26004, MR 1907120, 10.1016/S0022-247X(02)00049-5; reference:[14] Granas, A., Dugundji, J.: Fixed Point Theory. Springer-Verlag, New York, 2003. Zbl 1025.47002, MR 1987179, 10.1007/978-0-387-21593-8; reference:[15] Guo, D. J., Lakshmikantham, V., Liu, X.: Nonlinear Integral Equations in Abstract Spaces. Kluwer Academic Publishers, Dordrecht, 1996. Zbl 0866.45004, MR 1418859; reference:[16] Hadamard, J.: Essai sur l’étude des fonctions données par leur developpement de Taylor. J. Math. Pure Appl. Ser. 8 (1892), 101–186.; reference:[17] Kilbas, A. A., Srivastava, H. M., Trujillo, J. J.: Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies 204, Elsevier Science B.V., Amsterdam, 2006. Zbl 1092.45003, MR 2218073; reference:[18] Kilbas, A. A., Trujillo, J. J.: Hadamard-type integrals as G-transforms. Integral Transform. Spec. Funct. 14 (2003), 413–427. Zbl 1043.26004, MR 2005999, 10.1080/1065246031000074443; reference:[19] Lin, S.: Generalised Gronwall inequalities and their applications to fractional differential equations. J. Ineq. Appl. 2013, 549 (2013), 1–9. MR 3212979; reference:[20] Mönch, H.: Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces. Nonlinear Anal. 4 (1980), 985–999. MR 0586861, 10.1016/0362-546X(80)90010-3; reference:[21] Nieto, J. J., Ouahab, A., Venktesh, V.: Implicit fractional differential equations via the Liouville–Caputo derivative. Mathematics 3, 2 (2015), 398–411. Zbl 1322.34012, 10.3390/math3020398; reference:[22] Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego, 1999. Zbl 0924.34008, MR 1658022; reference:[23] Sun, S., Zhao, Y., Han, Z., Li, Y.: The existence of solutions for boundary value problem of fractional hybrid differential equations. Commun. Nonlinear Sci. Numer. Simul. 17 (2012), 4961–4967. Zbl 1352.34011, MR 2960290, 10.1016/j.cnsns.2012.06.001; reference:[24] Tarasov, V. E.: Fractional Dynamics: Application of Fractional Calculus to Dynamics of particles, Fields and Media. Springer & Higher Education Press, Heidelberg & Beijing, 2010. MR 2796453; reference:[25] Yosida, K.: Functional Analysis. 6th edn., Springer-Verlag, Berlin, 1980. Zbl 0435.46002, MR 0617913; reference:[26] Zhao, Y., Sun, S., Han, Z., Li, Q.: Theory of fractional hybrid differential equations. Comput. Math. Appl. 62 (2011), 1312–1324. Zbl 1228.45017, MR 2824718, 10.1016/j.camwa.2011.03.041

الاتاحة: http://hdl.handle.net/10338.dmlcz/145812