Existence and uniqueness of a positive solution to generalized nonlocal thermistor problems with fractional-order derivatives

In this work we study a generalized nonlocal thermistor problem with fractional-order Riemann-Liouville derivative. Making use of fixed-point theory, we obtain existence and uniqueness of a positive solution.Comment: Submitted 17-Jul-2011; revised 09-Oct-2011; accepted 21-Oct-2011; for publication in the journal 'Differential Equations & Applications' (http://dea.ele-math.com

Existence of solutions for hybrid differential equation with fractional order

In this paper, we study the existence of solutions for the following fractional hybrid differential equations involving Riemann-Liouville differential operators of order . An existence theorem for fractional hybrid differential equations is proved under mixed Lipschitz and Carathéodory conditions and using the Dhage point fixe theorem. Keywords: Quadratic perturbations;  Riemann-Liouville derivative;  Hybrid differential equation

Boundary value problem solving for semilinear fractional differential equations with nonlocal and integral boundary conditions

In this paper, we will study a boundary value problem for semilinear fractional differential equations of order q ∈ (1, 2] with nonlocal and integral boundary conditions. Some existence and uniqueness results with illustrative examples will be presented by applying some fixed point theorems.Publisher's Versio

Some existence results for impulsive nonlinear fractional differential equations with mixed boundary conditions

AbstractThis paper investigates the existence and uniqueness of solutions for an impulsive mixed boundary value problem of nonlinear differential equations of fractional order α∈(1,2]. Our results are based on some standard fixed point theorems. Some examples are presented to illustrate the main results

Theory of fractional hybrid differential equations

AbstractIn this paper, we develop the theory of fractional hybrid differential equations involving Riemann–Liouville differential operators of order 0<q<1. An existence theorem for fractional hybrid differential equations is proved under mixed Lipschitz and Carathéodory conditions. Some fundamental fractional differential inequalities are also established which are utilized to prove the existence of extremal solutions. Necessary tools are considered and the comparison principle is proved which will be useful for further study of qualitative behavior of solutions