Invariant solutions of hyperbolic fuzzy fractional differential equations

2019 ◽  
Vol 34 (01) ◽  
pp. 2050015 ◽  
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.

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

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.

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

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Abdourazek Souahi ◽  
Assia Guezane-Lakoud ◽  
Amara Hitta
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Arbitrary Order ◽  
Integral Form ◽  
Fractional Differential ◽  
Uniqueness And Existence ◽  
Fuzzy Fractional Differential Equations ◽  
Fuzzy Fractional Differential Equation

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.

Two-point boundary value problems for the generalized Bagley-Torvik fractional differential equation

2013 ◽  
Vol 11 (3) ◽  
Author(s):  
Svatoslav Staněk
Keyword(s):  
Differential Equation ◽  
Fractional Derivative ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Existence Results ◽  
Point Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Carathéodory Function ◽  
Fractional Differential

AbstractWe investigate the fractional differential equation u″ + A c D α u = f(t, u, c D μ u, u′) subject to the boundary conditions u′(0) = 0, u(T)+au′(T) = 0. Here α ∈ (1, 2), µ ∈ (0, 1), f is a Carathéodory function and c D is the Caputo fractional derivative. Existence and uniqueness results for the problem are given. The existence results are proved by the nonlinear Leray-Schauder alternative. We discuss the existence of positive and negative solutions to the problem and properties of their derivatives.

scholarly journals A New Impulsive Multi-Orders Fractional Differential Equation Involving Multipoint Fractional Integral Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Guotao Wang ◽  
Sanyang Liu ◽  
Dumitru Baleanu ◽  
Lihong Zhang
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Fractional Differential Equation ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential

A new impulsive multi-orders fractional differential equation is studied. The existence and uniqueness results are obtained for a nonlinear problem with fractional integral boundary conditions by applying standard fixed point theorems. An example for the illustration of the main result is presented.

scholarly journals Implicit fractional differential equation with nonlocal integral-multipoint boundary conditions in the frame of Hilfer fractional derivative

2021 ◽  
Vol 2 (1) ◽  
pp. 62-71
Author(s):  
Saleh Redhwan ◽  
Sadikali L. Shaikh
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Fractional Derivative ◽  
Fractional Differential Equation ◽  
Hilfer Fractional Derivative ◽  
Multipoint Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Multipoint Boundary Conditions ◽  
Fractional Differential

This article deals with a nonlinear implicit fractional differential equation with nonlocal integral-multipoint boundary conditions in the frame of Hilfer fractional derivative. The existence and uniqueness results are obtained by using the fixed point theorems of Krasnoselskii and Banach. Further, to demonstrate the effectiveness of the main results, suitable examples are granted.

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

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.

scholarly journals Existence and Uniqueness of Solutions for Coupled Impulsive Fractional Pantograph Differential Equations with Antiperiodic Boundary Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Karim Guida ◽  
Lahcen Ibnelazyz ◽  
Khalid Hilal ◽  
Said Melliani
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential ◽  
Banach’S Contraction Principle

In this paper, we investigate the solutions of coupled fractional pantograph differential equations with instantaneous impulses. The work improves some existing results and contributes toward the development of the fractional differential equation theory. We first provide some definitions that will be used throughout the paper; after that, we give the existence and uniqueness results that are based on Banach’s contraction principle and Krasnoselskii’s fixed point theorem. Two examples are given in the last part to support our study.

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