Investigation of the existence and uniqueness of solutions for higher order fractional differential inclusions and equations with integral boundary conditions

Lachouri, Adel; Ardjouni, Abdelouaheb; Djoudi, Ahcéne

doi:10.1080/09720529.2021.1877901

Cited by 8 publications

(5 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The differential equations, specially a fractional and ordinary, have motivated a number of researchers to explore the topic's theoretical and practical aspects. For more details, see previous works, 21,[23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] and the reader can also look up the references cited in the papers.…”

Section: 𝜇([0 𝜍]) = 𝜇({0}) + ∫ [0𝜍]mentioning

confidence: 99%

Existence and uniqueness of solutions of differential equations with respect to non‐additive measures

Negi

Torra

2022

Math Methods in App Sciences

View full text Add to dashboard Cite

Funding informationKempe foundation (Kempestiftelserna 891 80 Örnsköldsvik); Knut and Alice Wallenberg Foundation By taking Sugeno-derivative into account, first, we investigate the existence of solutions to the initial value problems (IVP) of first-order differential equations with respect to non-additive measure (more precisely, distorted Lebesgue measure). It particularly occurs in the mathematical modeling of biology. We begin by expressing the differential equation in terms of ordinary derivative and the derivative with respect to the distorted Lebesgue measure. Then, by using the fixed point theorem on cones, we construct an operator and prove the existence of positive non-decreasing solutions on cones in semi-order Banach spaces. In addition, we also use Picard-Lindelöf theorem to prove the existence and uniqueness of the solution of the equation.Second, we investigate the existence of a solution to the boundary value problem (BVP) on cones with integral boundary conditions of a mix-order differential equation with respect to non-additive measures. Moreover, the Krasnoselskii fixed point theorem is also applied to both BVP and IVP and obtains at least one positive non-decreasing solution. Examples with graphs are provided to validate the results.

show abstract

Section: 𝜇([0 𝜍]) = 𝜇({0}) + ∫ [0𝜍]mentioning

confidence: 99%

Existence and uniqueness of solutions of differential equations with respect to non‐additive measures

Negi

Torra

2022

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…Several researchers have focused on some fascinating outcomes of solutions to FDEs with beginning and boundary conditions by applying various FPTs (see [27][28][29]). Many studies on FPTs, topology, and nonlinear analysis have contributed to the current rapid growth of FDEs with HFD (see [30][31][32]).…”

Section: Introductionmentioning

confidence: 99%

On Some Impulsive Fractional Integro-Differential Equation with Anti-Periodic Conditions

Alruwaily,

Venkatachalam,

El-hady

2024

Fractal Fract

View full text Add to dashboard Cite

We investigate a class of boundary value problems (BVPs) involving an impulsive fractional integro-differential equation (IF-IDE) with the Caputo–Hadamard fractional derivative (C-HFD). We employ some fixed-point theorems (FPTs) to study the existence of this fractional BVP and its unique solution. The boundary conditions (BCs) established in this study are of a more general type and can be reduced to numerous specific examples by defining the parameters involved in the conditions. In this way, we extend some recent nice results. At the end, we use an example to verify our results.

show abstract

“…We now list a generalization of fractional derivatives, which is for Ψ-Caputo, which are for Caputo fractional derivatives and also Riemann-Liouville derivatives. The study conducted by reference [23] explores the existence and uniqueness of mild solutions of BVPs associated with Caputo-Hadamard fractional differential equations, incorporating integral and anti-periodic conditions.…”

Section: Introductionmentioning

confidence: 99%

On the Existence and Ulam Stability of BVP within Kernel Fractional Time

Saber,

Imsatfia,

Boulares

et al. 2023

Fractal Fract

View full text Add to dashboard Cite

This manuscript, we establish novel findings regarding the existence of solutions for second-order fractional differential equations employing Ψ-Caputo fractional derivatives. The application of Banach’s fixed-point theorem (BFPT) ensures the uniqueness of the solutions, while Schauder’s fixed-point theorem (SFPT) is instrumental in determining the existence of these solutions. Furthermore, we assess the stability of the proposed equation using the Ulam–Hyers stability criterion. To illustrate our results, we provide a concrete example showcasing their practical implications.

show abstract

Investigation of the existence and uniqueness of solutions for higher order fractional differential inclusions and equations with integral boundary conditions

Cited by 8 publications

References 26 publications

Existence and uniqueness of solutions of differential equations with respect to non‐additive measures

Existence and uniqueness of solutions of differential equations with respect to non‐additive measures

On Some Impulsive Fractional Integro-Differential Equation with Anti-Periodic Conditions

On the Existence and Ulam Stability of BVP within Kernel Fractional Time

Contact Info

Product

Resources

About