In this paper, we investigate the existence, uniqueness and stability of periodic solution of new integro-differential equations depended on special function with singular kernels. | Periodic solution of integro-differential equations depended on special function with singular Kernels International Journal of Mechanical Engineering and Technology IJMET Volume 10 Issue 03 March 2019 pp. 1681 1695 Article ID IJMET_10_03_170 Available online at http ijmet JType IJMET amp VType 10 amp IType 3 ISSN Print 0976-6340 and ISSN Online 0976-6359 IAEME Publication Scopus Indexed PERIODIC SOLUTION OF INTEGRO- DIFFERENTIAL EQUATIONS DEPENDED ON SPECIAL FUNCTION WITH SINGULAR KERNELS Raad N. Butris and Raveen F. Taher University of Duhok College of Basic Education Department of Mathematics Kurdistan Region Iraq ABSTRACT In this paper we investigate the existence uniqueness and stability of periodic solution of new integro-differential equations depended on special function with singular kernels. The numerical-analytic method has been used to study the periodic solutions for the ordinary differential equations that were introduced by Samoilenko. Also these investigation lead us to the improving and extending the results of Butris and extended Samoilenko method. Key words Numerical-analytic methods existence uniqueness and stability periodic solution integro-differential equations special function singular kernels Cite this Article Raad N. Butris and Raveen F. Taher Periodic Solution of Integro- Differential Equations Depended on Special Function with Singular Kernels International Journal of Mechanical Engineering and Technology 10 3 2019 pp. 1681 1695. http IJMET JType IJMET amp VType 10 amp IType 3 1. INTRODUCTION Many results about the existence and approximation of periodic solutions of integro- differential equations have been obtained by the numerical-analytic methods that were proposed by Samoilenko 18 which had been later applied in many subjects in physics and technology using mathematical methods that depends on the linear and nonlinear integro- differential equations and it became clear that the .
