scholarly journals Existence and Ulam–Hyers Stability of a Fractional-Order Coupled System in the Frame of Generalized Hilfer Derivatives

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2543
Author(s):  
Abdulkafi M. Saeed ◽  
Mohammed S. Abdo ◽  
Mdi Begum Jeelani
Keyword(s):  
Fixed Point ◽  
Fractional Order ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Coupled System ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Special Cases ◽  
Stability Of The Solution

In this research paper, we consider a class of a coupled system of fractional integrodifferential equations in the frame of Hilfer fractional derivatives with respect to another function. The existence and uniqueness results are obtained in weighted spaces by applying Schauder’s and Banach’s fixed point theorems. The results reported here are more general than those found in the literature, and some special cases are presented. Furthermore, we discuss the Ulam–Hyers stability of the solution to the proposed system. Some examples are also constructed to illustrate and validate the main results.

scholarly journals On Caputo–Riemann–Liouville Type Fractional Integro-Differential Equations with Multi-Point Sub-Strip Boundary Conditions

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1899
Author(s):  
Ahmed Alsaedi ◽  
Amjad F. Albideewi ◽  
Sotiris K. Ntouyas ◽  
Bashir Ahmad
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Liouville Type ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

In this paper, we derive existence and uniqueness results for a nonlinear Caputo–Riemann–Liouville type fractional integro-differential boundary value problem with multi-point sub-strip boundary conditions, via Banach and Krasnosel’skii⏝’s fixed point theorems. Examples are included for the illustration of the obtained results.

scholarly journals Existence and Uniqueness with Ulam Stability study of the solution for a class of Caputo fractional integro-differential equation with mixed conditions

2021 ◽  
Author(s):  
ABDELLOUAHAB Naimi
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Stability Study ◽  
Ulam Stability ◽  
Differential Problem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Stability Results

In this article we show the existence, uniqueness and Ulam stability results of the solution for a class of a nonlinear Caputo fractional integro-differential problem with mixed conditions. we use three fixed point theorems to proof the existence and uniqueness results. By the results obtained, the reasons for the Ulam stability are verified. An example proposed to illustrate our main results.

scholarly journals QUALITATIVE STUDY OF NONLINEAR COUPLED PANTOGRAPH DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040045 ◽  
Author(s):  
ISRAR AHAMAD ◽  
KAMAL SHAH ◽  
THABET ABDELJAWAD ◽  
FAHD JARAD
Keyword(s):  
Fixed Point ◽  
Qualitative Study ◽  
Differential Equations ◽  
Nonlinear Analysis ◽  
Fractional Order ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Coupled System ◽  
Main Work ◽  
Nonlinear Coupled System

In this paper, we investigate a nonlinear coupled system of fractional pantograph differential equations (FPDEs). The respective results address some adequate results for existence and uniqueness of solution to the problem under consideration. In light of fixed point theorems like Banach and Krasnoselskii’s, we establish the required results. Considering the tools of nonlinear analysis, we develop some results regarding Ulam–Hyers (UH) stability. We give three pertinent examples to demonstrate our main work.

scholarly journals Existence and Uniqueness Results of Volterra–Fredholm Integro-Differential Equations via Caputo Fractional Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Ameth Ndiaye ◽  
Fulgence Mansal
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Ulam Stability ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
The Fixed Point Theorem ◽  
Banach Principle ◽  
Stability Of The Solution

In this paper, we study a Volterra–Fredholm integro-differential equation. The considered problem involves the fractional Caputo derivatives under some conditions on the order. We prove an existence and uniqueness analytic result by application of the Banach principle. Then, another result that deals with the existence of at least one solution is delivered, and some sufficient conditions for this result are established by means of the fixed point theorem of Schaefer. Ulam stability of the solution is discussed before including an example to illustrate the results of the proposal.

scholarly journals Notes on Local and Nonlocal Intuitionistic Fuzzy Fractional Boundary Value Problems with Caputo Fractional Derivatives

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Ali El Mfadel ◽  
Said Melliani ◽  
M’hamed Elomari
Keyword(s):  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Caputo Fractional Derivatives ◽  
Existence And Uniqueness Results ◽  
Intuitionistic Fuzzy ◽  
Uniqueness Results ◽  
Fractional Boundary Value Problems

In this paper, we investigate the existence and uniqueness results of intuitionistic fuzzy local and nonlocal fractional boundary value problems by employing intuitionistic fuzzy fractional calculus and some fixed-point theorems. As an application, we conclude this manuscript by giving an example to illustrate the obtained results.

Existence and uniqueness results for a class of BVPs for nonlinear fractional differential equations

2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Djamal Foukrach ◽  
Toufik Moussaoui ◽  
Sotiris K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonlinear Fractional Differential Equations ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential

AbstractThis paper studies some new existence and uniqueness results for boundary value problems for nonlinear fractional differential equations by using a variety of fixed point theorems. Some illustrative examples are also presented.

Existence of solutions of BVPs for fractional Langevin equations involving Caputo fractional derivatives

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Zohre Kiyamehr ◽  
Hamid Baghani
Keyword(s):  
Fixed Point ◽  
Continuous Function ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Existence Of Solutions ◽  
Langevin Equations ◽  
Point Boundary ◽  
Caputo Fractional Derivatives ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

AbstractThis article investigates a nonlinear fractional Caputo–Langevin equationD^{\beta}(D^{\alpha}+\lambda)x(t)=f(t,x(t)),\quad 0<t<1,\,0<\alpha\leq 1,\,1<% \beta\leq 2,subject to the multi-point boundary conditionsx(0)=0,\qquad\mathcal{D}^{2\alpha}x(1)+\lambda\mathcal{D^{\alpha}}x(1)=0,% \qquad x(1)=\int_{0}^{\eta}x(\tau)\,d\tau\quad\text{for some }0<\eta<1,where {D^{\alpha}} is the Caputo fractional derivative of order α, {f:[0,1]\times\mathbb{R}\to\mathbb{R}} is a given continuous function, and λ is a real number. Some new existence and uniqueness results are obtained by applying an interesting fixed point theorem.

scholarly journals Existence and uniqueness results for Φ-Caputo implicit fractional pantograph differential equation with generalized anti-periodic boundary condition

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Idris Ahmed ◽  
Poom Kumam ◽  
Thabet Abdeljawad ◽  
Fahd Jarad ◽  
Piyachat Borisut ◽  
...  
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Uniqueness Of Solutions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Special Cases ◽  
Generalized Fractional Derivative

Abstract The present paper describes the implicit fractional pantograph differential equation in the context of generalized fractional derivative and anti-periodic conditions. We formulated the Green’s function of the proposed problems. With the aid of a Green’s function, we obtain an analogous integral equation of the proposed problems and demonstrate the existence and uniqueness of solutions using the techniques of the Schaefer and Banach fixed point theorems. Besides, some special cases that show the proposed problems extend the current ones in the literature are presented. Finally, two examples were given as an application to illustrate the results obtained.

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