Discontinuity, Nonlinearity, and Complexity
Existence Results of Fractional Neutral Integrodifferential Equations with Deviating Arguments
Discontinuity, Nonlinearity, and Complexity 9(2) (2020) 277287  DOI:10.5890/DNC.2020.06.008
B. Kamalapriya, K. Balachandran, N. Annapoorani
Department of Mathematics, Bharathiar University, Coimbatore 641046, India
Download Full Text PDF
Abstract
In this paper we prove the existence of solutions of fractional neutral integrodifferential equations with deviating arguments by using the resolvent operators and fixed point theorem. Examples are discussed to illustrate the theory.
References

[1]  Kilbas, A.A., Srivastava, H.M., and Trujillo, J.J. (2006), Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam. 

[2]  Miller, K.S. and Ross, B. (1993), An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York. 

[3]  Podlubny, I. (1999), Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, New York: Academic Press. 

[4]  Banas, J. (1986), An existence theorem for nonlinear volterra integral equation with deviating argument, Rendiconti Del Circolo Matematico di Palermo, 8289. 

[5]  Balachandran, K. and Ilamaran, S. (1990), An existence theorem for a Volterra integral equations with deviating arguments, Journal of Applied Mathematics and Stochastic Analysis, 3, 155162. 

[6]  Balachandran, K. and Kiruthika, S. (2011), Existence results for fractional integrodifferential equations with nonlocal condition via resolvent operators, Computers and Mathematics with Applications, 62, 13501358. 

[7]  Balachandran, K., Kiruthika, S., Rivero, M., and Trujillo, J.J. (2012), Existence of solutions for fractional delay integrodifferential equations, Journal of Applied Nonlinear Dynamics, 1, 309319. 

[8]  Hernandez, E., O’Regan, D., and Balachandran, K. (2010), On recent developments in the theory of abstract differential equations with fractional derivatives, Nonlinear Analysis 73, 34623471. 

[9]  Hernandez, E., O’Regan, D., and Balachandran, K. (2013), Existence results for abstract fractional differential equations with nonlocal conditions via resolvent operators, Indagationes Mathematicae, 24, 6882. 

[10]  Byszewski, L. (1991), Theorems about existence and uniqueness of a solution of a semilinear evolution nonlocal Cauchy problem, Journal of Mathematical Analysis and Applications, 162, 496505. 

[11]  Balachandran, K. and Trujillo, J.J. (2010), The nonlocal Cauchy problem for nonlinear fractional integrodifferential equations in Banach spaces, Nonlinear Analysis: Theory, Methods and Applications, 72, 45874593. 

[12]  Kamalapriya, B., Balachandran, K., and Annapoorani, N. (2017), Existence results for fractional integrodifferential equations, Nonlinear Functional Analysis and Applications, 22(3), 641653. 

[13]  Joice Nirmala, R. and Balachandran, K. (2016), Controllability of nonlinear fractional delay integrodifferential systems, Discontinuity, Nonlinearity, and Complexity, 5, 5973. 

[14]  Balachandran, K. and Dauer, J.P. (1998), Existence of solutions of a nonlinear mixed neutral equations, Applied Mathematics Letters, 11, 2328. 

[15]  Balachandran, K. and Sakthivel, R. (1999), Existence of solutions of neutral functional integrodifferential equations in Banach spaces, Proceedings of the Indian Academic Sciences and Mathematical Sciences, 109, 325332. 

[16]  Dauer, J.P. and Balachandran, K. (2000), Existence of solutions of nonlinear neutral integrodifferential equations in Banach spaces, Journal of Mathematical Analysis and Applications, 251, 93105. 

[17]  Fu, X.L. and Ezzinbi, K. (2003), Existence of solutions for neutral functional differential evolution equations with nonlocal conditions, Nonlinear Analysis, 54, 215227. 

[18]  Pruss, J. (1993), Evolutionary Integral Equations and Applications, Birkhauser Verlag, Basel. 