Integral solutions of fractional neutral mixed type integro-differential systems with non-instantaneous impulses in Banach space

Downloads

Abstract

The main purpose of this article is to examine the existence and uniqueness of integral solutions for a class
of fractional order neutral mixed type integro-differential equations with non-instantaneous impulses and nondensely
defined linear operators in Banach spaces. Based on the Banach contraction principle, we develop the
main results.

Keywords:

Fractional neutral differential equations, mild solution, non-instantaneous impulses, fixed point theorem

Mathematics Subject Classification:

Mathematics
  • M. Mallika Arjunan Department of Mathematics, Vel Tech High Tech Dr. Rangarajan Dr. Sakunthala Engineering College, Avadi-600062, Tamil Nadu, India.
  • Pages: 244-246
  • Date Published: 01-01-2021
  • Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)

J. Bora and S.N. Bora, Sufficient conditions for existence of integral solution for non-instantaneous impulsive fractional evolution equations, Indian J. Pure Appl. Math., $51(3)(2020), 1065-1082$.

H. Gu, Y. Zhou, B. Ahmad and A. Alsaedi, Integral solutions of fractional evolution equations with nondense domain, Electron. J. Differential Equations, Vol. 2017 (2017), No. $145,1-15$.

X. Fu, X. Liu and B. Lu, On a new class of impulsive fractional evolution equations, Advances in Difference Equations, (2015) 2015:227.

E. Hernández and D. O'Regan, On a new class of abstract impulsive differential equations, Proc.Amer. Math. Soc., 141 (2013), 1641-1649.

M. Mallika Arjunan, Existence results for nonlocal fractional mixed type integro-differential equations with noninstantaneous impulses in Banach space, Malaya Journal of Matematik, 7(4)(2019), 837-840.

M. Mallika Arjunan, Integral solutions of fractional order mixed type integro-differential equations with noninstantaneous impulses in Banach space, Malaya Journal of Matematik, $8(4)(2020), 2212-2214$.

M. Mallika Arjunan, On fractional Volterra-Fredholm integro-differential systems with non-dense domain and non-instantaneous impulses, Malaya Journal of Matematik, $8(4)(2020), 2228-2232$.

B. Zhu, B. Han, L. Liu and W. Yu, On the fractional partial integro-differential equations of mixed type with non-instantaneous impulses, Boundary Value Problems, $(2020), 2020: 154$

A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, vol. 204. Elsevier, Amsterdam, 2006.

Y. Zhou and F. Jiao, Nonlocal Cauchy problem for fractional evolution equations, Nonlinear Anal., Real World Appl. 11(2010), 4465-4475.

Y. Zhou and F. Jiao, Existence of mild solutions for fractional neutral evolution equations, Comput. Math. Appl., $59(2010), 1063-1077$.

Metrics

Metrics Loading ...

Published

01-01-2021

How to Cite

M. Mallika Arjunan. “Integral Solutions of Fractional Neutral Mixed Type Integro-Differential Systems With Non-Instantaneous Impulses in Banach Space”. Malaya Journal of Matematik, vol. 9, no. 01, Jan. 2021, pp. 244-6, https://www.malayajournal.org/index.php/mjm/article/view/1007.