AM  Vol.4 No.7 A , July 2013
Mild Solutions of Fractional Semilinear Integro-Differential Equations on an Unbounded Interval
Abstract: In this paper, we study the existence of mild solutions for fractional semilinear integro-differential equations in an arbitrary Banach space associated with operators generating compact semigroup on the Banach space. The arguments are based on the Schauder fixed point theorem.
Cite this paper: A. Jawahdou, "Mild Solutions of Fractional Semilinear Integro-Differential Equations on an Unbounded Interval," Applied Mathematics, Vol. 4 No. 7, 2013, pp. 34-39. doi: 10.4236/am.2013.47A007.

[1]   R. P. Agarwal, M. Benchohra and S. A. Hamani, “Survey on the Existence Results for Boundary Value Problems of Nonlinear Fractional Differential Equations and Inclusions,” Acta Applicandae Mathematicae, Vol. 109, No. 3, 2010, pp. 973-1033. 0Hdoi:10.1007/s10440-008-9356-6

[2]   M. benchohra, J. Henderson and S. K. Ntouyas, “Impulsive Differential Equations and inclusions,” Hindawi Publishing Corporation, New York, 2006.

[3]   M. Benchohra and B. A. Slimani, “Existence and Uniqueness of Solutions to Impulsive Fractional Differential Equations,” Electronic Journal of Differential Equations, Vol. 10, 2009, pp. 1-11.

[4]   L. Byszewski, “Theorems about the Existence and Uniqueness of Solutions of a Semilinear Evolution Nonlocal Cauchy Problem,” Journal of Mathematical Analysis and Applications, Vol. 162, No. 18, 1991, pp. 494-505. 1Hdoi:10.1016/0022-247X(91)90164-U

[5]   A. Karczewska and S. Wedrychowicz, “Existence of Mild Solutions for Semilinear Equation of Evolution,” Commentationes Mathematicae Universitatis Carolinae, Vol. 37, No. 4, 1996, pp. 695-706.

[6]   J. Banas and K. Goebel, “Measures of Noncompactness in Banach Spaces, Lecture Notes in Pure and Applied Mathematics,” Marcel Dekker, New York, 1980.

[7]   J. Banas, “On Existence Theorems for Differential Equations in Banach Spaces,” Bulletin of the Australian Mathematical Society, Vol. 32, No. 01, 1985, pp. 73-82. 2Hdoi:10.1017/S0004972700009734

[8]   A. Jawahdou, “Mild Solutions of Functional Semilinear Evolution Volterra Integrodifferential Equations on an Unbounded Interval,” Nonlinear Analysis: Real World Applications, Vol. 74, No. 18, 2011, pp. 7325-7332. 3Hdoi:10.1016/

[9]   A. Jawahdou and A. Karoui, “Monotonic Solutions of Nonlinear Integral Equations of Fractional Order,” Canadian Applied Mathematics Quarterly, Vol. 18, No. 1, 2010, pp. 41-58.

[10]   L. Olszowy and S. Wedrychowicz, “Mild Solutions of Semilinear Evolution Equation on an Unbounded Interval and Their Applications,” Nonlinear Analysis: Real World Applications, Vol. 72, No. 3, 2010, pp. 2119-2126. 4Hdoi:10.1016/

[11]   L. V. Kantorovich and G. P. Akilov, “Functional Analysis in Normed Spaces,” Pergamon Press, Oxford, 1982.

[12]   M. W. Michalski, “Derivatives of Noninteger Order and Their Applications. Dissertationes Mathematicae, Polska Akademia Nauk,” Instytut Matematyczny, Warszawa, 1993.

[13]   C. Corduneanu, “Integral Equations and Applications,” Cambridge University Press, New York, 1990.

[14]   M. H. M. Rashid and Y. El-Qadri, “Semilinear Fractional Integro-Differential Equations with Compact Semigroup,” Nonlinear Analysis: Real World Applications, Vol. 71, No. 12, 2009, pp. 6276-6282. 5Hdoi:10.1016/