Existence and uniqueness results for nonlinear implicit Riemann-Liouville fractional differential equations with nonlocal conditions

Lachouri, Adel; Ardjouni, Abdelouaheb; Djoudi, Ahcéne

doi:10.2298/fil2014881l

Cited by 5 publications

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“…Finally, an example is given to illustrate our main results. Our results extend the main results of [30]. This paper will be organized as follows.…”

Section: Introductionsupporting

confidence: 84%

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Existence Results for Coupled Implicit \({\psi}\)-Riemann–Liouville Fractional Differential Equations with Nonlocal Conditions

Jiang

Bai

2022

Axioms

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In this paper, we study the existence and uniqueness of solutions for a coupled implicit system involving ψ-Riemann–Liouville fractional derivative with nonlocal conditions. We first transformed the coupled implicit problem into an integral system and then analyzed the uniqueness and existence of this integral system by means of Banach fixed-point theorem and Krasnoselskiis fixed-point theorem. Some known results in the literature are extended. Finally, an example is given to illustrate our theoretical result.

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“…Finally, an example is given to illustrate our main results. Our results extend the main results of [30]. This paper will be organized as follows.…”

Section: Introductionsupporting

confidence: 84%

“…Very recently, in [30], Lachouri et al studied the existence and uniqueness of solutions for the following nonlinear implicit Riemann-Liouville fractional differential equation with nonlocal condition:…”

Section: Introductionmentioning

confidence: 99%

Existence Results for Coupled Implicit \({\psi}\)-Riemann–Liouville Fractional Differential Equations with Nonlocal Conditions

Jiang

Bai

2022

Axioms

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“…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

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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.

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“…In this sense, several interesting topics concerning research for differential equations involving fractional quantum calculus have been devoted to the existence and the Ulam-Hyers stability of the solutions. Recently, many interesting results concerning the existence and Ulam-type stability of solutions for differential equations with fractional q-calculus have been obtained, see [8][9][10][11] and the references therein. In [12,13], the existence and uniqueness of solutions were investigated for sequential differential equations with q-fractional calculus.…”

Section: Introductionmentioning

confidence: 99%

Existence and stability analysis for a class of fractional pantograph q-difference equations with nonlocal boundary conditions

2023

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In this present manuscript, by applying fractional quantum calculus, we study a nonlinear fractional pantograph q-difference equation with nonlocal boundary conditions. We prove the existence and uniqueness results by using the well-known fixed-point theorems of Schaefer and Banach. We also discuss the Ulam–Hyers stability of the mentioned pantograph q-difference problem. Lastly, the paper includes pertinent examples to support our theoretical analysis and justify the validity of the results.

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Existence and uniqueness results for nonlinear implicit Riemann-Liouville fractional differential equations with nonlocal conditions

Abstract: In this paper, we use the fixed point theory to obtain the existence and uniqueness of solutions for nonlinear implicit Riemann-Liouville fractional differential equations with nonlocal conditions. An example is given to illustrate this work.

Cited by 5 publications

References 0 publications

Existence Results for Coupled Implicit \({\psi}\)-Riemann–Liouville Fractional Differential Equations with Nonlocal Conditions

Existence Results for Coupled Implicit \({\psi}\)-Riemann–Liouville Fractional Differential Equations with Nonlocal Conditions

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

Existence and stability analysis for a class of fractional pantograph q-difference equations with nonlocal boundary conditions

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