scholarly journals Fuzzy Conformable Fractional Differential Equations

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 .

scholarly journals Existence and uniqueness theorem for a solution of fuzzy differential equations

1999 ◽  
Vol 22 (2) ◽  
pp. 271-279 ◽  
Author(s):  
Jong Yeoul Park ◽  
Hyo Keun Han
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Differential Equations ◽  
Uniqueness Theorem ◽  
Successive Approximation ◽  
Existence And Uniqueness ◽  
Fuzzy Differential Equation ◽  
Existence And Uniqueness Theorem ◽  
Uniqueness Of A Solution

By using the method of successive approximation, we prove the existence and uniqueness of a solution of the fuzzy differential equationx′(t)=f(t,x(t)),x(t0)=x0. We also consider anϵ-approximate solution of the above fuzzy differential equation.

scholarly journals Complex Transforms for Systems of Fractional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
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.

Monotone iterative technique for impulsive Riemann-Liouville fractional differential equations

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3381-3395 ◽  
Author(s):  
Renu Chaudhary ◽  
Dwijendra Pandey
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Measure Of Noncompactness ◽  
Semigroup Theory ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Monotone Iterative ◽  
Fractional Differential

In this article, Monotone iterative technique coupled with the method of lower and upper solutions is employed to discuss the existence and uniqueness of mild solution to an impulsive Riemann-Liouville fractional differential equation. The results are obtained using the concept of measure of noncompactness, semigroup theory and generalized Gronwall inequality for fractional differential equations. At last, an example is given to illustrate the applications of the main results.

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.

scholarly journals On existence–uniqueness results for proportional fractional differential equations and incomplete gamma functions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Zaid Laadjal ◽  
Thabet Abdeljawad ◽  
Fahd Jarad
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Uniqueness Of Solutions ◽  
Gamma Functions ◽  
Uniqueness Results ◽  
Incomplete Gamma Functions ◽  
Fractional Differential ◽  
Derivatives Of

AbstractIn this article, we employ the lower regularized incomplete gamma functions to demonstrate the existence and uniqueness of solutions for fractional differential equations involving nonlocal fractional derivatives (GPF derivatives) generated by proportional derivatives of the form $$ D^{\rho }= (1-\rho )+ \rho D, \quad \rho \in [0,1], $$ D ρ = ( 1 − ρ ) + ρ D , ρ ∈ [ 0 , 1 ] , where D is the ordinary differential operator.

scholarly journals Ulam Stability of n-th Order Delay Integro-Differential Equations

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3029
Author(s):  
Shuyi Wang ◽  
Fanwei Meng
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Mathematical Induction ◽  
Ulam Stability ◽  
Existence And Uniqueness Theorem ◽  
Integro Differential Equation ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In this paper, the Ulam stability of an n-th order delay integro-differential equation is given. Firstly, the existence and uniqueness theorem of a solution for the delay integro-differential equation is obtained using a Lipschitz condition and the Banach contraction principle. Then, the expression of the solution for delay integro-differential equation is derived by mathematical induction. On this basis, we obtain the Ulam stability of the delay integro-differential equation via Gronwall–Bellman inequality. Finally, two examples of delay integro-differential equations are given to explain our main results.

scholarly journals ON THE NONLINEAR IMPULSIVE Ψ–HILFER FRACTIONAL DIFFERENTIAL EQUATIONS

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.

Cauchy problem for an ordinary fractional differential equation with variable delay

2021 ◽  
Vol 21 (3) ◽  
pp. 16-20
Author(s):  
M.G. Mazhgikhova ◽  
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Uniqueness Theorem ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Initial Problem ◽  
Variable Delay ◽  
Existence And Uniqueness Theorem ◽  
Method Of Steps ◽  
Fractional Differential

For a fractional differential equation with variable delay, a solution to the initial problem is obtained by the method of steps. The existence and uniqueness theorem of the solution is proved.

scholarly journals An Extension of the Picard Theorem to Fractional Differential Equations with a Caputo-Fabrizio Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
H. R. Marasi ◽  
A. Soltani Joujehi ◽  
H. Aydi
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Approximation Method ◽  
Existence And Uniqueness ◽  
Successive Approximation Method ◽  
Existence And Uniqueness Theorem ◽  
Initial Value ◽  
Picard Theorem ◽  
Fractional Differential

In this paper, we consider fractional differential equations with the new fractional derivative involving a nonsingular kernel, namely, the Caputo-Fabrizio fractional derivative. Using a successive approximation method, we prove an extension of the Picard-Lindelöf existence and uniqueness theorem for fractional differential equations with this derivative, which gives a set of conditions, under which a fractional initial value problem has a unique solution.

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