On the Existence and Uniqueness for High Order Fuzzy Fractional Differential Equations with Uncertainty

A class fuzzy fractional differential equation (FFDE) involving Riemann-LiouvilleH-differentiability of arbitrary orderq>1is considered. Using Krasnoselskii-Krein type conditions, Kooi type conditions, and Rogers conditions we establish the uniqueness and existence of the solution after determining the equivalent integral form of the solution.

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Existence, Uniqueness, and Eq–Ulam-Type Stability of Fuzzy Fractional Differential Equation

Fractal and Fractional ◽

10.3390/fractalfract5030066 ◽

2021 ◽

Vol 5 (3) ◽

pp. 66

Author(s):

Azmat Ullah Khan Niazi ◽

Jiawei He ◽

Ramsha Shafqat ◽

Bilal Ahmed

Keyword(s):

Differential Equation ◽

Cauchy Problem ◽

Fractional Differential Equation ◽

Existence And Uniqueness ◽

Initial Conditions ◽

The Cauchy Problem ◽

Fractional Differential ◽

Ulam Type Stability ◽

Fuzzy Fractional Differential Equations ◽

Fuzzy Fractional Differential Equation

This paper concerns with the existence and uniqueness of the Cauchy problem for a system of fuzzy fractional differential equation with Caputo derivative of order q∈(1,2], 0cD0+qu(t)=λu(t)⊕f(t,u(t))⊕B(t)C(t),t∈[0,T] with initial conditions u(0)=u0,u′(0)=u1. Moreover, by using direct analytic methods, the Eq–Ulam-type results are also presented. In addition, several examples are given which show the applicability of fuzzy fractional differential equations.

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Fuzzy Conformable Fractional Differential Equations

International Journal of Differential Equations ◽

10.1155/2021/6655450 ◽

2021 ◽

Vol 2021 ◽

pp. 1-6

Author(s):

Atimad Harir ◽

Said Melliani ◽

Lalla Saadia Chadli

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Uniqueness Theorem ◽

Fractional Differential Equations ◽

Existence And Uniqueness ◽

Existence And Uniqueness Theorem ◽

Fractional Differential ◽

Fractional Differentiability ◽

Derivatives Of ◽

Fuzzy Fractional Differential Equation

In this study, fuzzy conformable fractional differential equations are investigated. We study conformable fractional differentiability, and we define fractional integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy fractional differential equation by using the concept of conformable differentiability. This concept is based on the enlargement of the class of differentiable fuzzy mappings; for this, we consider the lateral Hukuhara derivatives of order q ∈ 0,1 .

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Invariant solutions of hyperbolic fuzzy fractional differential equations

Modern Physics Letters B ◽

10.1142/s0217984920500153 ◽

2019 ◽

Vol 34 (01) ◽

pp. 2050015 ◽

Cited By ~ 2

Author(s):

C. Vinothkumar ◽

J. J. Nieto ◽

A. Deiveegan ◽

P. Prakash

Keyword(s):

Differential Equation ◽

Fractional Differential Equation ◽

Numerical Solutions ◽

Banach Fixed Point Theorem ◽

Invariant Solutions ◽

Existence And Uniqueness Results ◽

Uniqueness Results ◽

Fractional Differential ◽

Fuzzy Fractional Differential Equations ◽

Fuzzy Fractional Differential Equation

We consider the hyperbolic type fuzzy fractional differential equation and derive the second-order fuzzy fractional differential equation using scaling transformation. We present a theoretical and a numerical method to find the invariant solutions of such equations. Also, we prove the existence and uniqueness results using Banach fixed point theorem. Numerical solutions are approximated using finite difference method. Finally, numerical examples are given to illustrate the obtained results.

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Complex Transforms for Systems of Fractional Differential Equations

Abstract and Applied Analysis ◽

10.1155/2012/814759 ◽

2012 ◽

Vol 2012 ◽

pp. 1-15 ◽

Cited By ~ 3

Author(s):

Rabha W. Ibrahim

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Fractional Differential Equation ◽

Fractional Differential Equations ◽

Existence And Uniqueness ◽

Uniqueness Of Solutions ◽

Fractional Differential

We provide a complex transform that maps the complex fractional differential equation into a system of fractional differential equations. The homogeneous and nonhomogeneous cases for equivalence equations are discussed and also nonequivalence equations are studied. Moreover, the existence and uniqueness of solutions are established and applications are illustrated.

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ON THE NONLINEAR IMPULSIVE Ψ–HILFER FRACTIONAL DIFFERENTIAL EQUATIONS

Mathematical Modelling and Analysis ◽

10.3846/mma.2020.11445 ◽

2020 ◽

Vol 25 (4) ◽

pp. 642-660

Author(s):

Kishor D. Kucche ◽

Jyoti P. Kharade ◽

J. Vanterler da C. Sousa

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Fractional Differential Equation ◽

Fractional Differential Equations ◽

Existence And Uniqueness ◽

Uniqueness Of Solutions ◽

Fractional Differential

In this paper, we consider the nonlinear Ψ-Hilfer impulsive fractional differential equation. Our main objective is to derive the formula for the solution and examine the existence and uniqueness of solutions. The acquired results are extended to the nonlocal Ψ-Hilfer impulsive fractional differential equation. We gave an applications to the outcomes we obtained. Further, examples are provided in support of the results we got.

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Solutions for impulsive fractional pantograph differential equation via generalized anti-periodic boundary condition

Advances in Difference Equations ◽

10.1186/s13662-020-02887-4 ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Idris Ahmed ◽

Poom Kumam ◽

Jamilu Abubakar ◽

Piyachat Borisut ◽

Kanokwan Sitthithakerngkiet

Keyword(s):

Differential Equation ◽

Boundary Condition ◽

Fixed Point ◽

Fractional Differential Equation ◽

Existence And Uniqueness ◽

Periodic Boundary Condition ◽

Periodic Boundary ◽

Fixed Point Theorems ◽

Uniqueness Of The Solution ◽

Fractional Differential

Abstract This study investigates the solutions of an impulsive fractional differential equation incorporated with a pantograph. This work extends and improves some results of the impulsive fractional differential equation. A differential equation of an impulsive fractional pantograph with a more general anti-periodic boundary condition is proposed. By employing the well-known fixed point theorems of Banach and Krasnoselskii, the existence and uniqueness of the solution of the proposed problem are established. Furthermore, two examples are presented to support our theoretical analysis.

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An estimation of effects of memory and learning experience on the eoq model with price dependent demand

RAIRO - Operations Research ◽

10.1051/ro/2021127 ◽

2021 ◽

Vol 55 (5) ◽

pp. 2991-3020

Author(s):

Mostafijur Rahaman ◽

Sankar Prasad Mondal ◽

Shariful Alam

Keyword(s):

Differential Equation ◽

Decision Making ◽

Fractional Differential Equation ◽

Lot Sizing ◽

Learning Experience ◽

Memory And Learning ◽

Eoq Model ◽

Novel Approach ◽

Fractional Differential ◽

Fuzzy Fractional Differential Equation

In this article, an economic order quantity model has been studied in view of joint impacts of the memory and learning due to experiences on the decision-making process where demand is considered as price dependant function. The senses of memory and experience-based learning are accounted by the fractional calculus and dense fuzzy lock set respectively. Here, the physical scenario is mathematically captured and presented in terms of fuzzy fractional differential equation. The α-cut defuzzification technique is used for dealing with the crisp representative of the objective function. The main credit of this article is the introduction of a smart decision-making technique incorporating some advanced components like memory, self-learning and scopes for alternative decisions to be accessed simultaneously. Besides the dynamics of the EOQ model under uncertainty is described in terms of fuzzy fractional differential equation which directs toward a novel approach for dealing with the lot-sizing problem. From the comparison of the numerical results of different scenarios (as particular cases of the proposed model), it is perceived that strong memory and learning experiences with appropriate keys in the hand of the decision maker can boost up the profitability of the retailing process.

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