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EFFECT OF PERTURBATION IN THE SOLUTION OF FRACTIONAL NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

  • ABDO, MOHAMMED. S. (RESEARCH SCHOLAR AT DEPARTMENT OF MATHEMATICS, DR. BABASAHEB AMBEDKAR MARATHWADA UNIVERSITY) ;
  • PANCHAL, SATISH. K. (DEPARTMENT OF MATHEMATICS, DR. BABASAHEB AMBEDKAR MARATHWADA UNIVERSITY)
  • Received : 2018.01.07
  • Accepted : 2018.03.12
  • Published : 2018.03.25

Abstract

In this paper, we study the initial value problem for neutral functional differential equations involving Caputo fractional derivative of order ${\alpha}{\in}(0,1)$ with infinite delay. Some sufficient conditions for the uniqueness and continuous dependence of solutions are established by virtue of fractional calculus and Banach fixed point theorem. Some results obtained showed that the solution was closely related to the conditions of delays and minor changes in the problem. An example is provided to illustrate the main results.

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