THEORY OF FRACTIONAL IMPLICIT DIFFERENTIAL EQUATIONS WITH COMPLEX ORDER

Authors : Elsayed Elsayed, D. Vivek, K. Kanagarajan

Pages : 154-165

Doi:10.33773/jum.577349

View : 11 | Download : 5

Publication Date : 2019-07-29

Article Type : Research

Abstract :In this paper, we consider boundary value problems for the following nonlinear implicit differential  equations with complex order   D +x(t) = f t,x(t),D +x(t) , ? = m+i?, t ? J := [0,T],   ax(0)+bx(T) = c, where D + is the Caputo fractional derivative of order ? ? C. Let ? ? R , 0 < ? < 1, m ? (0,1], and  f : J ×R ? R is given continuous function. Here a,b,c are real constants with a+b  = 0.  We derive the existence and stability of solution for a class of boundary value problem(BVP) for  nonlinear fractional implicit differential equations(FIDEs) with complex order. The results are based  upon the Banach contraction principle and Schaefer’s fixed point theorem.
Keywords : Implicit differential equation, Boundary value problem, Stirling asymptotic formula