Existence theory for implicit fractional q-difference equations in Banach spaces

Impulsive Fractional Differential Equations in Banach Spaces

This paper is devoted to study the existence of solutions for a class of initial value problems for impulsive fractional differential equations involving the Caputo fractional derivative in a Banach space. The arguments are based upon Mönch’s fixed point theorem and the technique of measures of noncompactness.

Existence results for fractional neutral functional integro-differential evolution equations with infinite delay in Banach spaces

*Correspondence: [email protected] 2Department of Mathematics and Computer Science, Faculty of Arts and Sciences, Cankaya University, Ankara, 06530, Turkey 3Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia Full list of author information is available at the end of the article Abstract In this paper, we investigate the...

Fractional relaxation equations on Banach spaces

We study existence and qualitative properties of solutions for the abstract fractional relaxation equation (0.1) u′(t)−ADα t u(t) + u(t) = f(t), 0 < α < 1, t ≥ 0, u(0) = 0, on a complex Banach space X, where A is a closed linear operator, Dα t is the Caputo derivative of fractional order α ∈ (0, 1), and f is an X-valued function. We also study conditions under which the solution operator has th...

An Existence Result for Nonlinear Fractional Differential Equations on Banach Spaces

Monotone Iterative Technique for Fractional Evolution Equations in Banach Spaces

We investigate the initial value problem for a class of fractional evolution equations in a Banach space. Under some monotone conditions and noncompactness measure conditions of the nonlinearity, the well-known monotone iterative technique is then extended for fractional evolution equations which provides computable monotone sequences that converge to the extremal solutions in a sector generate...