Analysis of Impulsive Boundary Value Pantograph Problems via Caputo Proportional Fractional Derivative under Mittag–Leffler Functions

This manuscript investigates an extended boundary value problem for a fractional pantograph differential equation with instantaneous impulses under the Caputo proportional fractional derivative with respect to another function. The solution of the proposed problem is obtained using Mittag–Leffler functions. The existence and uniqueness results of the proposed problem are established by combining the well-known fixed point theorems of Banach and Krasnoselskii with nonlinear functional techniques. In addition, numerical examples are presented to demonstrate our theoretical analysis.

Download Full-text

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

Mathematics ◽

10.3390/math8111899 ◽

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.

Download Full-text

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

10.22541/au.161133857.79110223/v1 ◽

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.

Download Full-text

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

Advances in Mathematical Physics ◽

10.1155/2021/6616899 ◽

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.

Download Full-text

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

Journal of Mathematics ◽

10.1155/2021/5623388 ◽

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.

Download Full-text

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

Journal of Mathematics ◽

10.1155/2021/4322841 ◽

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.

Download Full-text

Tripled fixed point theorems and applications to a fractional differential equation boundary value problem

Asian-European Journal of Mathematics ◽

10.1142/s1793557117500565 ◽

2017 ◽

Vol 10 (03) ◽

pp. 1750056 ◽

Cited By ~ 1

Author(s):

Hojjat Afshari ◽

Alireza Kheiryan

Keyword(s):

Differential Equation ◽

Fixed Point ◽

Boundary Value Problem ◽

Fractional Differential Equation ◽

Existence And Uniqueness ◽

Fixed Point Theorems ◽

Boundary Value ◽

Tripled Fixed Point ◽

Equation Boundary ◽

Fractional Differential

In this article we study a class of mixed monotone operators with convexity on ordered Banach spaces and present some new tripled fixed point theorems by means of partial order theory, we get the existence and uniqueness of tripled fixed points without assuming the operator to be compact or continuous, which extend the existing corresponding results. As applications, we utilize the results obtained in this paper to study the existence and uniqueness of positive solutions for a fractional differential equation boundary value problem.

Download Full-text

Existence and Uniqueness Results for a Class of Singular Fractional Boundary Value Problems with the p-Laplacian Operator via the Upper and Lower Solutions Approach

Journal of Function Spaces ◽

10.1155/2020/2930892 ◽

2020 ◽

Vol 2020 ◽

pp. 1-15

Author(s):

KumSong Jong ◽

HuiChol Choi ◽

KyongJun Jang ◽

SunAe Pak

Keyword(s):

Fixed Point ◽

Boundary Value Problems ◽

Existence And Uniqueness ◽

Boundary Value ◽

Upper And Lower Solutions ◽

Gauss Hypergeometric Function ◽

Laplacian Operator ◽

Existence And Uniqueness Results ◽

Uniqueness Results ◽

Nonlinear Alternative

In this paper, we study the existence and uniqueness of positive solutions to a class of multipoint boundary value problems for singular fractional differential equations with the p-Laplacian operator. Here, the nonlinear source term f permits singularity with respect to its time variable t. Some fixed-point theorems such as the Leray-Schauder nonlinear alternative, the Schauder fixed-point theorem, and the Banach contraction mapping principle and the properties of the Gauss hypergeometric function are used to prove our main results. And by employing the upper and lower solutions technique, we derive a new approach to obtain the maximal and minimal solutions to the given problem. Finally, we present some examples to demonstrate our existence and uniqueness results.

Download Full-text

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

Georgian Mathematical Journal ◽

10.1515/gmj-2014-0054 ◽

2015 ◽

Vol 22 (1) ◽

Cited By ~ 2

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.

Download Full-text

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

Advances in Difference Equations ◽

10.1186/s13662-020-03008-x ◽

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.

Download Full-text

Nonlocal boundary value problems for ψ-Hilfer fractional-order Langevin equations

Boundary Value Problems ◽

10.1186/s13661-021-01511-y ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Cholticha Nuchpong ◽

Sotiris K. Ntouyas ◽

Devaraj Vivek ◽

Jessada Tariboon

Keyword(s):

Fractional Order ◽

Existence And Uniqueness ◽

Fixed Point Theorems ◽

Boundary Value ◽

Nonlocal Boundary ◽

Integral Boundary Conditions ◽

Langevin Equations ◽

Integral Boundary ◽

Existence And Uniqueness Results ◽

Uniqueness Results

AbstractIn the paper, we study a boundary value problem for a class of ψ-Hilfer fractional-order Langevin equations with multi-point integral boundary conditions. Existence and uniqueness results are established by using well-known fixed point theorems. Examples illustrating the main results are also included.

Download Full-text