scholarly journals Fuzzy Fractional Evolution Equations and Fuzzy Solution Operators

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Atimad Harir ◽  
Said Melliani ◽  
Lalla Saadia Chadli
Keyword(s):  
Fractional Derivative ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Fractional Evolution Equations ◽  
Fuzzy Solution ◽  
Definition Of ◽  
Fuzzy Laplace Transform ◽  
Derivative Order

In this paper, the fuzzy fractional evolution equations of order q (FFEE) with fuzzy Caputo fractional derivative are introduced. We study the existence and uniqueness of mild solutions for FFEE under some conditions. Also, we generalize the definition of the fuzzy fractional integral and derivative order q. The fuzzy Laplace transform is presented and proved. The solvability of the problem (FFEE) and the properties of the fuzzy solution operator and its generator are investigated and developed.

scholarly journals On the Existence and Uniqueness Results for Fuzzy Linear and Semilinear Fractional Evolution Equations Involving Caputo Fractional Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Ali El Mfadel ◽  
Said Melliani ◽  
M’hamed Elomari
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Existence Theorems ◽  
Fractional Evolution Equations ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Banach Contraction

In this manuscript, we establish new existence and uniqueness results for fuzzy linear and semilinear fractional evolution equations involving Caputo fractional derivative. The existence theorems are proved by using fuzzy fractional calculus, Picard’s iteration method, and Banach contraction principle. As application, we conclude this paper by giving an illustrative example to demonstrate the applicability of the obtained results.

scholarly journals Existence and Attractivity for Fractional Evolution Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Yong Zhou ◽  
Jia Wei He ◽  
Bashir Ahmad ◽  
Ahmed Alsaedi
Keyword(s):  
Fractional Derivative ◽  
Evolution Equations ◽  
Global Attractivity ◽  
Mild Solutions ◽  
Sufficient Conditions ◽  
Cauchy Problems ◽  
Fractional Evolution Equations ◽  
Liouville Fractional Derivative

We study the existence and attractivity of solutions for fractional evolution equations with Riemann-Liouville fractional derivative. We establish sufficient conditions for the global attractivity of mild solutions for the Cauchy problems in the case that semigroup is compact.

scholarly journals Mild Solutions for Impulsive Integro-Differential Equations Involving Hilfer Fractional Derivative with almost Sectorial Operators

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 313
Author(s):  
Kulandhaivel Karthikeyan ◽  
Panjaiyan Karthikeyan ◽  
Nichaphat Patanarapeelert ◽  
Thanin Sitthiwirattham
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Jump Conditions ◽  
Hilfer Fractional Derivative ◽  
Sectorial Operators ◽  
Almost Sectorial Operators ◽  
Suitable Definition ◽  
Definition Of

In this manuscript, we establish the mild solutions for Hilfer fractional derivative integro-differential equations involving jump conditions and almost sectorial operator. For this purpose, we identify the suitable definition of a mild solution for this evolution equations and obtain the existence results. In addition, an application is also considered.

Existence of mild solutions for a class of Hilfer fractional evolution equations with nonlocal conditions

2017 ◽  
Vol 20 (3) ◽  
Author(s):  
Min Yang ◽  
Qiru Wang
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Hilfer Fractional Derivative ◽  
Fractional Evolution Equations ◽  
Noncompact Measure ◽  
The Fixed Point Theorem ◽  
New Criteria

AbstractIn this paper, we consider a class of evolution equations with Hilfer fractional derivative. By employing the fixed point theorem and the noncompact measure method, we establish a number of new criteria to guarantee the existence and uniqueness of mild solutions when the associated semigroup is compact or not.

scholarly journals Optimal control of nonlocal fractional evolution equations in the α-norm of order $(1,2)$

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Azmat Ullah Khan Niazi ◽  
Naveed Iqbal ◽  
Wael W. Mohammed
Keyword(s):  
Optimal Control ◽  
Continuous Dependence ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Fractional Evolution Equations ◽  
Lagrange Problem ◽  
Adequate Definition ◽  
Fractional Evolution Systems ◽  
Definition Of ◽  
Evolution Systems

AbstractThis paper investigates the optimal control for a class of nonlocal fractional evolution equations of order $\gamma \in (1,2)$ γ ∈ ( 1 , 2 ) in Banach spaces. An adequate definition of α-mild solutions is obtained and the existence, uniqueness and continuous dependence of α-mild solutions for the presented control system are also established. The existence of optimal pairs of nonlocal fractional evolution systems is also demonstrated with a view on the construction of the Lagrange problem. Finally, an example is propounded for the presentation of optimal control.

scholarly journals Periodic Solutions andS-Asymptotically Periodic Solutions to Fractional Evolution Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Jia Mu ◽  
Yong Zhou ◽  
Li Peng
Keyword(s):  
Periodic Solutions ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Fractional Evolution Equations ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Asymptotically Periodic ◽  
Liouville Fractional Derivative ◽  
Asymptotically Periodic Solutions

This paper deals with the existence and uniqueness of periodic solutions,S-asymptotically periodic solutions, and other types of bounded solutions for some fractional evolution equations with the Weyl-Liouville fractional derivative defined for periodic functions. Applying Fourier transform we give reasonable definitions of mild solutions. Then we accurately estimate the spectral radius of resolvent operator and obtain some existence and uniqueness results.

scholarly journals Positive Mild Solutions of Periodic Boundary Value Problems for Fractional Evolution Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Jia Mu ◽  
Hongxia Fan
Keyword(s):  
Existence And Uniqueness ◽  
Periodic Boundary ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Boundary Value ◽  
Fractional Evolution Equations ◽  
Existence And Uniqueness Results ◽  
Monotone Iterative ◽  
Uniqueness Results ◽  
Periodic Boundary Value Problems

The periodic boundary value problem is discussed for a class of fractional evolution equations. The existence and uniqueness results of mild solutions for the associated linear fractional evolution equations are established, and the spectral radius of resolvent operator is accurately estimated. With the aid of the estimation, the existence and uniqueness results of positive mild solutions are obtained by using the monotone iterative technique. As an application that illustrates the abstract results, an example is given.

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

2014 ◽  
Vol 17 (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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