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Some theorems on fractional semilinear evolution equations

Tidke H. L.

Journal of Applied Analysis

2012

Vol. 18, nr 2

209-224

In this paper, we investigate the existence, uniqueness and other properties of solutions of fractional semilinear evolution equations in Banach spaces. The results are obtained by using fractional calculus, the well-known Banach fixed point theorem coupled with Bielecki type norm and the integral inequality established by E. Hernandez.

Existence and uniqueness of solution of differential equation of second order in cone metric spaces

Tidke H. L., Dhakne M. B.

Fasciculi Mathematici

2010

Nr 45

121-131

In this paper we investigate the existence and uniqueness for fractional and non-fractional dierential equations in cone metric spaces. The result is obtained by using the some extensions of Banach's contraction principle in complete cone metric space, fractional calculus and the theory of strongly continuous cosine family.

Existence and uniqueness of mild and strong solutions of nonlinear Volterra integrodifferential equations in Banach spaces

Tidke H. L., Dhakne M. B.

Demonstratio Mathematica

2010

Vol. 43, nr 3

643-652

In this paper we prove the existence and uniqueness of mild and strong solutions of a nonlinear Volterra integrodifferential equation with nonlocal condition. Our analysis is based on semigroup theory and Banach fixed point theorem and inequalities are established by Gronwall and B. G. Pachpatte.