Mild solutions in Besov or Morrey spaces

Abstract In this paper, we obtain generalized weighted Sobolev-Morrey estimates with weights from the Muckenhoupt class Ap by establishing boundedness of several important operators in harmonic analysis such as Hardy-Littlewood operators and Calderon-Zygmund singular integral operators in generalized weighted Morrey spaces. As a consequence, a priori estimates for the weak solutions Dirichlet boundary problem uniformly elliptic equations of higher order in generalized weighted Sobolev-Morrey spaces in a smooth bounded domain Ω ⊂ ℝn are obtained.

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MILD SOLUTIONS OF A FRACTIONAL PDE WITH NOISE

Authorea ◽

10.22541/au.158379380.03193207 ◽

2020 ◽

Author(s):

Noureddine Bouteraa ◽

Mustafa Inc ◽

Mehmet Ali Akinlar

Keyword(s):

Mild Solutions ◽

Fractional Pde

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On fractional differential equations with state-dependent delay via Kuratowski measure of noncompactness

Filomat ◽

10.2298/fil1702451b ◽

2017 ◽

Vol 31 (2) ◽

pp. 451-460 ◽

Cited By ~ 1

Author(s):

Mohammed Belmekki ◽

Kheira Mekhalfi

Keyword(s):

Differential Equations ◽

Measure Of Noncompactness ◽

Mild Solutions ◽

Functional Differential Equations ◽

Kuratowski Measure Of Noncompactness ◽

State Dependent ◽

State Dependent Delay ◽

Liouville Fractional Derivative ◽

Fractional Differential ◽

Functional Differential

This paper is devoted to study the existence of mild solutions for semilinear functional differential equations with state-dependent delay involving the Riemann-Liouville fractional derivative in a Banach space and resolvent operator. The arguments are based upon M?nch?s fixed point theoremand the technique of measure of noncompactness.

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Existence results of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay

Fractional Calculus and Applied Analysis ◽

10.2478/s13540-014-0219-8 ◽

2014 ◽

Vol 17 (4) ◽

Cited By ~ 4

Author(s):

Shengli Xie

Keyword(s):

Differential Equations ◽

Differential Evolution ◽

Existence Theorem ◽

Banach Spaces ◽

Existence And Uniqueness ◽

Evolution Equations ◽

Infinite Delay ◽

Mild Solutions ◽

Existence Results ◽

Order Case

AbstractIn this paper we prove the existence and uniqueness of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay in Banach spaces. We generalize the existence theorem for integer order differential equations to the fractional order case. The results obtained here improve and generalize many known results.

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Nonlocal fractional semilinear differential inclusions with noninstantaneous impulses and of order α ∈ (1, 2)

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2019-0179 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

JinRong Wang ◽

Ahmed G. Ibrahim ◽

Donal O’Regan ◽

Adel A. Elmandouh

Keyword(s):

Differential Inclusions ◽

Mild Solutions ◽

Multivalued Function ◽

Linear Operators ◽

Solution Set ◽

Cosine Family ◽

Bounded Linear Operators ◽

Bounded Linear ◽

Noninstantaneous Impulses

AbstractIn this paper, we establish the existence of mild solutions for nonlocal fractional semilinear differential inclusions with noninstantaneous impulses of order α ∈ (1,2) and generated by a cosine family of bounded linear operators. Moreover, we show the compactness of the solution set. We consider both the case when the values of the multivalued function are convex and nonconvex. Examples are given to illustrate the theory.

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