Fractional evolution equation nonlocal problems with noncompact semigroups

Solutions to Nonlocal Fractional Differential Equations Using a Noncompact Semigroup

This article concerns the existence of solutions to nonlocal fractional differential equations in Banach spaces. By using a type of newly-defined measure of noncompactness, we discuss this problem in general Banach spaces without any compactness assumptions to the operator semigroup. Some existence results are obtained when the nonlocal term is compact and when is Lipschitz continuous.

Complex Fuzzy Evolution Equation with Nonlocal Conditions

The objective of this paper is to study the existence and uniqueness of Mild solutions for a complex fuzzy evolution equation with nonlocal conditions that accommodates the notion of fuzzy sets defined by complex-valued membership functions. We first propose definition of complex fuzzy strongly continuous semigroups. We then give existence and uniqueness result relevant to the complex fuzzy evo...

Solvability of Nonlocal Fractional Boundary Value Problems

Fractional Evolution Integro-Differential Systems with Nonlocal Conditions

In this paper, we use the theory of resolvent operators, the fractional powers of operators, fixed point technique and the Gelfand–Shilov principle to establish the existence and uniqueness of local mild and then local classical solutions of a class of nonlinear fractional evolution integro-differential systems with nonlocal conditions in Banach space. As an application that illustrates the abs...

Positive solutions for nonlocal boundary value problems of fractional differential equation

Abstract: In this paper, we investigate the existence, uniqueness and multiplicity of positive solutions for nonlocal boundary value problems of fractional differential equation. Firstly, we reduce the problem considered to the equivalent integral equation. Secondly, the existence and uniqueness of positive solution is obtained by the use of contraction map principle and some Lipschitz-type con...