Systems of implicit fractional fuzzy differential equations with nonlocal conditions

Mild Solutions for Fractional Differential Equations with Nonlocal Conditions

This paper is concerned with the existence and uniqueness of mild solution of the fractional differential equations with nonlocal conditions d q xt/dt q −Axt ft, xt, Gxt, t ∈ 0, T, and x0 gx x 0 , in a Banach space X, where 0 < q < 1. General existence and uniqueness theorem, which extends many previous results, are given.

On mild solutions to fractional differential equations with nonlocal conditions

We prove new existence results of mild solutions to fractional differential equations with nonlocal conditions in Banach spaces. The nonlocal item is only assumed to be continuous. This generalizes some recent results in this area.

Fuzzy Local Fractional Differential Equations

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...

Integro-differential Equations of Fractional Order with Nonlocal Fractional Boundary Conditions Associated with Financial Asset Model

In this article, we discuss the existence of solutions for a boundaryvalue problem of integro-differential equations of fractional order with nonlocal fractional boundary conditions by means of some standard tools of fixed point theory. Our problem describes a more general form of fractional stochastic dynamic model for financial asset. An illustrative example is also presented. 1. Formulation ...