THEORY OF FRACTIONAL IMPLICIT DIFFERENTIAL EQUATIONS WITH COMPLEX ORDER

Yıl 2019, Cilt: 2 Sayı: 2, 154 - 165, 29.07.2019

Elsayed Elsayed , D. Vivek , K. Kanagarajan

https://doi.org/10.33773/jum.577349

Cited By: 3

Öz

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.

Anahtar Kelimeler

Implicit differential equation, Boundary value problem, Stirling asymptotic formula

Kaynakça

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