2,710 research outputs found
On initial and boundary value problems for fractional order mixed type functional differential inclusions
AbstractIn this paper we prove some existence results for initial and boundary value problems for functional differential inclusions of fractional order with both retarded and advanced arguments. The Banach fixed point theorem, the nonlinear alternative of the Leray–Schauder type and the Covitz–Nadler fixed point theorem are the main tools in deriving our proofs
Well-posedness via Monotonicity. An Overview
The idea of monotonicity (or positive-definiteness in the linear case) is
shown to be the central theme of the solution theories associated with problems
of mathematical physics. A "grand unified" setting is surveyed covering a
comprehensive class of such problems. We elaborate the applicability of our
scheme with a number examples. A brief discussion of stability and
homogenization issues is also provided.Comment: Thoroughly revised version. Examples correcte
A survey on fuzzy fractional differential and optimal control nonlocal evolution equations
We survey some representative results on fuzzy fractional differential
equations, controllability, approximate controllability, optimal control, and
optimal feedback control for several different kinds of fractional evolution
equations. Optimality and relaxation of multiple control problems, described by
nonlinear fractional differential equations with nonlocal control conditions in
Banach spaces, are considered.Comment: This is a preprint of a paper whose final and definite form is with
'Journal of Computational and Applied Mathematics', ISSN: 0377-0427.
Submitted 17-July-2017; Revised 18-Sept-2017; Accepted for publication
20-Sept-2017. arXiv admin note: text overlap with arXiv:1504.0515
On the Nonlinear Impulsive --Hilfer Fractional Differential Equations
In this paper, we consider the nonlinear -Hilfer impulsive fractional
differential equation. Our main objective is to derive the formula for the
solution and examine the existence and uniqueness of results. The acquired
results are extended to the nonlocal -Hilfer impulsive fractional
differential equation. We gave an applications to the outcomes we procured.
Further, examples are provided in support of the results we got.Comment: 2
Ulam Stabilities for Partial Impulsive Fractional Differential Equations
summary:In this paper we investigate the existence of solutions for the initial value problems (IVP for short), for a class of implicit impulsive hyperbolic differential equations by using the lower and upper solutions method combined with Schauder’s fixed point theorem
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