Existence of solution to a class of fractional delay differential equation under multi-points boundary conditions

Ali, Gauhar; Shah, Kamal; Rahman, Ghaus ur

doi:10.1080/25765299.2020.1850621

Cited by 11 publications

(4 citation statements)

References 38 publications

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“…Proof. Suppose (V 1 , V 2 ) ∈ X × X to be the solution of the problem Equation (28). Then, by corollary, (1), we have…”

Section: Stability Analysismentioning

confidence: 99%

“…In this connection, the existence and uniqueness of a solution studied by various techniques, such as monotone iterative technique, were discussed in [22]; topological degree theory was the concern in [23]; a method of successive approximation was developed in [24]; fixed point index theory was used in [25], and tools of fixed point theory (FPT) were used in [26]. For more details, see the recent work cited as [27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

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Formulation, Solution’s Existence, and Stability Analysis for Multi-Term System of Fractional-Order Differential Equations

2022

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In the recent past, multi-term fractional equations have been studied using symmetry methods. In some cases, many practical test problems with some symmetries are provided to demonstrate the authenticity and utility of the used techniques. Fractional-order differential equations can be formulated by using two types of differential operators: single-term and multi-term differential operators. Boundary value problems with single- as well as multi-term differential operators have been extensively studied, but several multi-term fractional differential equations still need to be formulated, and examination should be done with symmetry or any other feasible techniques. Therefore, the purpose of the present research work is the formulation and study of a new couple system of multi-term fractional differential equations with delay, as well as supplementation with nonlocal boundary conditions. After model formulation, the existence of a solution and the uniqueness conditions will be developed, utilizing fixed point theory and functional analysis. Moreover, results related to Ulam’s and other types of functional stability will be explored, and an example is carried out to illustrate the findings of the work.

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“…Proof. Suppose (V 1 , V 2 ) ∈ X × X to be the solution of the problem Equation (28). Then, by corollary, (1), we have…”

Section: Stability Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Formulation, Solution’s Existence, and Stability Analysis for Multi-Term System of Fractional-Order Differential Equations

2022

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“…Since then, Hyers [8] refined the Ulam-Hyers stability, and Rassias [9] further developed the Ulam-Hyers-Rassias stability. At present, researchers have made progress in studying the existence and Ulam stability analysis of fractional differential equations (see [10][11][12][13][14]). We note that there are few results on fractional differential equations with multiple terms.…”

Section: Introductionmentioning

confidence: 99%

The Existence and Ulam Stability Analysis of a Multi-Term Implicit Fractional Differential Equation with Boundary Conditions

Wang,

Han,

Bao

2024

Fractal Fract

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In this paper, we investigate a class of multi-term implicit fractional differential equation with boundary conditions. The application of the Schauder fixed point theorem and the Banach fixed point theorem allows us to establish the criterion for a solution that exists for the given equation, and the solution is unique. Afterwards, we give the criteria of Ulam–Hyers stability and Ulam–Hyers–Rassias stability. Additionally, we present an example to illustrate the practical application and effectiveness of the results.

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“…The concerned fractional order PDEs have been studied recently for existence theory in [33,34]. Also continuous type delay problems of FODEs have been studied recently for theoretical analysis, we refer the reader to [35][36][37]. Furthermore, in [38], the authors have investigated the following problem under APBCs with 0 < δ < 1:…”

Section: Introductionmentioning

confidence: 99%

Study of a nonlinear multi-terms boundary value problem of fractional pantograph differential equations

et al. 2021

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In this research work, a class of multi-term fractional pantograph differential equations (FODEs) subject to antiperiodic boundary conditions (APBCs) is considered. The ensuing problem involves proportional type delay terms and constitutes a subclass of delay differential equations known as pantograph. On using fixed point theorems due to Banach and Schaefer, some sufficient conditions are developed for the existence and uniqueness of the solution to the problem under investigation. Furthermore, due to the significance of stability analysis from a numerical and optimization point of view Ulam type stability and its various forms are studied. Here we mention different forms of stability: Hyers–Ulam (HU), generalized Hyers–Ulam (GHU), Hyers–Ulam Rassias (HUR) and generalized Hyers–Ulam–Rassias (GHUR). After the demonstration of our results, some pertinent examples are given.

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Existence of solution to a class of fractional delay differential equation under multi-points boundary conditions

Cited by 11 publications

References 38 publications

Formulation, Solution’s Existence, and Stability Analysis for Multi-Term System of Fractional-Order Differential Equations

Formulation, Solution’s Existence, and Stability Analysis for Multi-Term System of Fractional-Order Differential Equations

The Existence and Ulam Stability Analysis of a Multi-Term Implicit Fractional Differential Equation with Boundary Conditions

Study of a nonlinear multi-terms boundary value problem of fractional pantograph differential equations

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