Some results on fractional semilinear impulsive integro-differential equations

S. Suresh; G. Thamizhendhi

doi:10.26637/MJM0702/0017

Abstract

This paper is devoted to study the existence and uniqueness of solution for non-local impulsive fractional integro-differential equations involving the Caputo fractional derivative in a Banach Space. The arguments are based upon contraction mapping principle and Krasnoselskii’s fixed point theorem.

Keywords:

Fractional integro-differential equations, Fixed point methods, Impulsive condition

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

S. Suresh Department of Mathematics, Kongu Arts and Science College, Erode, Tamilnadu, India.
G. Thamizhendhi Department of Mathematics, Vellalar College for Women, Erode, Tamilnadu, India.

Pages: 259-263
Date Published: 01-04-2019
Vol. 7 No. 02 (2019): Malaya Journal of Matematik (MJM)

A.Anguraj, M.Kasthuri, P. Karthikeyan, Existence of solutions for impulsive fractional differential equations with anti-periodic and integral jump conditions, Nonlinear Studies, 24(3)(2017), 501-510.

R. P. Agarwal, M. Benchohra and S. Hamani, Boundary value problems for fractional differential equations, Advanced Studies in Contemporary Mathematics, $16(2)(2008), 181-196$.

G. Akram and F. Anjum, Existence and uniqueness of solution for differential equation of fractional order $2

A. Chauhan and J. Dabas, Studied the existence of mild solutions for impulsive fractional- order semilinear evoluation equations with nonlocal conditions, Electronic journal of Differential Equations, 2011(2011), 1-10.

K.Balachandran and J.Y.Park, Nonlocal Cauchy problem for abstract fractional semilinear evolution equation, Nonlinear Analysis, 71(2009), 4471-4475.

D. D. Bainov, P. S. Simeonov, Systems with Impulsive effect, Horwood, Chichister, 1989.

B. Ahmad And S. Sivasundaram, Some existence results for fractional integro - differetial equations with nonlinear conditions, Communications in Applied Analysis, $12(2)(2008), 107-112$.

M. Benchohra, J. R. Graef and S. Hamani, Existence results for boundary value problems with nonlinear fractional differential equations, Journal of Applied Analysis, $87(7)(2008), 851-863$.

M. Benchohra, J. Henderson and S. K. Ntouyas, Impulsive Differential Equations and Inclusions, Hindawi Publishing Corporation, 2(2006).

D. Delbosco and L. Rodino, Existence and uniqueness for a nonlinear fractional differential equation, Journal of Mathematical Analysis and Applications, 204(1996), $609-625$.

V. Gupta, J. Dabas, and M. Feckan, Existence results of solutions for impulsive fractional differential equations, Nonautonomous Dynamical Systems, 5(2018), 35-51.

W. G. Glockle and T. F. Nonnenmacher, A fractional calculus approach of self-similar protein dynamics, Biophysical Journal, 68(1995), 46-53.

R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.

A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, 204. Elsevier, Amsterdam, 2006.

V. Lakshmikantham, D. D. Bainov and P. S. Simeonov, Theory of Impulsive Differential Equations, Worlds Scientific, Singapore, 1989.

F. Metzler, W. Schick, H. G. Kilian and T. F. Nonnenmacher, Relaxation in filled polymers: A fractional calculus approach, Journal of Chemical Physics, 103(1995), $7180-7186$

K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Differential Equations, John Wiley, New York, 1993.

P. Karthikeyan, R.Arul, Existence of solutions for Hadamard fractional hybrid differential equations with impulsive and nonlocal conditions, Journal of Fractional Calculus and Applications, 9(1)(2018), 232-240.

K. B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, New York, London, 1974.

I. Podlubny, Fractional Differential Equation, Academic Press, San Diego, 1999.

S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach, Yverdon, 1993.

A. M. Samoilenko, N. A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, 1995.

C. Yu and G. Gao, Existence of fractional differential equations, Journal of Mathematical Analysis and Applications, 310(2005), 26-29.

Z.W. Lv, J. Liang and T.J Xiao, Solutions to Fractional Differential Equations with nonlocal initial condition in Banach Space, Advances in Difference Equations, $2010(2010), 1-10$.

Z. Dahmani and $mathrm{S}$. Belarbi, New results for fractional evolution equations using Banach fixed point theorem, International Journal of Nonlinear Analysis and Applications, $5(2)(2014), 22-30$.