Jñānābha‎, Vol. 48 (2) (2018), 46-58

DHAGE ITERATION METHOD FOR IVPS OF NONLINEAR SECOND ORDER HYBRID FUNCTIONAL INTEGRODIFFERENTIAL EQUATIONS OF NEUTRAL TYPE

Bapurao C. Dhage1, Shyam B. Dhage2 and Sidharth D. Sarkate3
1Kasubai, Gurukul Colony, Ahmedpur-413 515, Dist: Latur, Maharashtra, India,
Email:bcdhage@gmail.com
2Kasubai, Gurukul Colony, Ahmedpur-413 515, Dist: Latur, Maharashtra, India,
Email:sbdhage4791@gmail.com
3Department of Mathematics, Millind College of Science, Nagsenvana, Aurangabad-431001, 
Maharashtra, India 
Email:sdsarkate@gmail.com 
(Received : November 06, 2018; Revised: November 25, 2018)



Abstract

In this paper we prove an existence and approximation result for a second order initial value problems of nonlinear hybrid functional integrodifferential equations of neutral type via construction of an algorithm. The main results rely on the Dhage iteration method embodied in a recent hybrid .fixed point principle of Dhage (2015) and includes the existence and approximation theorems for several functional differential equations considered earlier in the literature. An example is also furnished to illustrate the hypotheses and the abstract result of this paper.

2010 Mathematics Subject Classifications: 34A12, 34A45, 47H07, 47H10.
Keywords and phrases: Hybrid neutral functional differential equation, Hybrid fixed point principle, Dhage iteration method, Existence and Approximation theorem.