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EXISTENCE AND STABILITY RESULTS OF GENERALIZED FRACTIONAL INTEGRODIFFERENTIAL EQUATIONS
C. Kausika,K. Balachandran,N. Annapoorani,J. K. Kim 경남대학교 수학교육과 2021 Nonlinear Functional Analysis and Applications Vol.26 No.4
This paper gives sufficient conditions to ensure the existence and stability of solutions for generalized nonlinear fractional integrodifferential equations of order $\alpha$ ($1 < \alpha < 2$). The main theorem asserts the stability results in a weighted Banach space, employing the Krasnoselskii's fixed point technique and the existence of at least one mild solution satisfying the asymptotic stability condition. Two examples are provided to illustrate the theory.
P. Umamaheswari,K. Balachandran,N. Annapoorani,김대욱 경남대학교 수학교육과 2023 Nonlinear Functional Analysis and Applications Vol.28 No.2
In this paper we prove the existence and uniqueness of solution of stochastic fractional neutral differential equations with Gaussian noise or Lévy noises by using the Picar-Lindelöf successive approximation scheme. Further stability results of nonlinear stochastic fractional dynamical system with Gaussian and Lévy noises are established. Examples are provided to illustrate the theoretical results.
Existence results for impulsive neutral functional integrodifferential equations with infinite delay
Park, J.Y.,Balachandran, K.,Annapoorani, N. Pergamon Press 2009 Nonlinear analysis Vol.71 No.7
This paper is concerned with the existence of mild solutions for impulsive neutral functional integrodifferential equations with infinite delay in Banach spaces. The results are obtained by using the Krasnoselski-Schaefer type fixed point theorem. An example is provided to illustrate the theory.