On Hadamard fractional integro-differential boundary value problems
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Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)
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)
Baleanu, D., Diethelm, K., Scalas, E., Trujillo, J.J.: Fractional Calculus Models and Numerical Methods. Series on Complexity, Nonlinearity and Chaos, World Scientific, Boston (2012)
Agarwal, R.P., Zhou, Y., He, Y.: Existence of fractional neutral functional differential equations. Comput. Math. Appl. 59, 1095–1100 (2010)
Baleanu, D., Mustafa, O.G., Agarwal, R.P.: On L $$^p$$ p -solutions for a class of sequential fractional differential equations. Appl. Math. Comput. 218, 2074–2081 (2011)
Ahmad, B., Nieto, J.J.: Riemann–Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions. Bound. Value Probl. 36, 9 (2011)
Ahmad, B., Ntouyas, S.K., Alsaedi, A.: New existence results for nonlinear fractional differential equations with three-point integral boundary conditions. Adv. Differ. Equ. 2011, 11 (2011). Article ID 107384
O’Regan, D., Stanek, S.: Fractional boundary value problems with singularities in space variables. Nonlinear Dyn. 71, 641–652 (2013)
Ahmad, B., Ntouyas, S.K., Alsaedi, A.: A study of nonlinear fractional differential equations of arbitrary order with Riemann–Liouville type multistrip boundary conditions. Math. Probl. Eng. 2013, 9 (2013). Article ID 320415
Ahmad, B., Nieto, J.J.: Boundary value problems for a class of sequential integrodifferential equations of fractional order. J. Funct. Spaces Appl. 2013, 8 (2013). Article ID 149659
Zhang, L., Ahmad, B., Wang, G., Agarwal, R.P.: Nonlinear fractional integro-differential equations on unbounded domains in a Banach space. J. Comput. Appl. Math. 249, 51–56 (2013)
Liu, X., Jia, M., Ge, W.: Multiple solutions of a p-Laplacian model involving a fractional derivative. Adv. Differ. Equ. 2013, 126 (2013)
Zhong, W., Yang, X., Gao, F.: A Cauchy problem for some local fractional abstract differential equation with fractal conditions. J. Appl. Funct. Anal. 8, 92–99 (2013)
Hadamard, J.: Essai sur l’etude des fonctions donnees par leur developpment de Taylor. J. Mat. Pure Appl. Ser. 8, 101–186 (1892)
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, 387–400 (2002)
Butzer, P.L., Kilbas, A.A., Trujillo, J.J.: Fractional calculus in the Mellin setting and Hadamard-type fractional integrals. J. Math. Anal. Appl. 269, 1–27 (2002)
Butzer, P.L., Kilbas, A.A., Trujillo, J.J.: Mellin transform analysis and integration by parts for Hadamard-type fractional integrals. J. Math. Anal. Appl. 270, 1–15 (2002)
Kilbas, A.A.: Hadamard-type fractional calculus. J. Korean Math. Soc. 38, 1191–1204 (2001)
Kilbas, A.A., Trujillo, J.J.: Hadamard-type integrals as G-transforms. Integr. Transform. Spec. Funct. 14, 413–427 (2003)
Krasnoselskii, M.A.: Two remarks on the method of successive approximations. Uspekhi Mat. Nauk 10, 123–127 (1955)