No abstract

No abstract

The Banach fixed point theorem and the nonlinear alternative of Leray-Schauder type are used to investigate the existence of solutions for fractional order functional and neutral functional differential equations with infinite delay.

No abstract

In this paper we initiate the study of quantum calculus on finite intervals. We define the q k -derivative and q k -integral of a function and prove their basic properties. As an application, we prove existence and uniqueness results for initial value problems for first-and second-order impulsive q k -difference equations.

In this paper, some of the most important integral inequalities of analysis are extended to quantum calculus. These include the Hölder, Hermite-Hadamard, trapezoid, Ostrowski, Cauchy-Bunyakovsky-Schwarz, Grüss, and Grüss-Čebyšev integral inequalities. The analysis relies on the notions of q-derivative and q-integral on finite intervals introduced by the authors in (Tariboon and Ntouyas in Adv. Differ.

No abstract

This paper is concerned with the existence and uniqueness of solutions for a coupled system of Hadamard type fractional differential equations and integral boundary conditions. We emphasize that much work on fractional boundary value problems involves either Riemann-Liouville or Caputo type fractional differential equations. In the present work, we have considered a new problem which deals with a system of Hadamard differential equations and Hadamard type integral boundary conditions. The existence of solutions is derived from Leray-Schauder's alternative, whereas the uniqueness of solution is established by Banach's contraction principle. An illustrative example is also included.MSC 2010 : Primary 34A08; Secondary 34A12, 34B15