On the Existence and Stability of Boundary Value Problem for Differential Equation with Hilfer-Katugampola Fractional Derivative

Elsayed, E. M.; Harikrishnan, S.; Kanagarajan, K.

doi:10.1007/s10473-019-0608-5

Cited by 16 publications

(15 citation statements)

References 14 publications

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“…In the following definitions, the HU‐stability and the HUR‐stability of () are introduced, which are considered as the concepts in investigating the stability of functional equations in abstract spaces, 36,37 the stability of the Cauchy problem of differential equations, 38–40,45 and the stability of BVP‐FDEs 20,24 …”

Section: Preliminariesmentioning

confidence: 99%

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Hyers–Ulam stability for boundary value problem of fractional differential equations with κ‐Caputo fractional derivative

Rassias

Hoa

2022

Math Methods in App Sciences

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The purpose of this paper is to discuss basic results of boundary value problems of fractional differential equations (BVP-FDEs) via the concept of Caputo fractional derivative with respect to another function with the order 𝛼 ∈ (1, 2). The existence and uniqueness results of a solution for BVP-FDEs are discussed by utilizing Banach fixed point theorem and Schaefer's fixed point theorem. We also provide new sufficient conditions to guarantee the Hyers-Ulam stability and the Hyers-Ulam-Rassias stability of BVP-FDEs. Furthermore, some concrete examples to consolidate the obtained results are also considered.

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Section: Preliminariesmentioning

confidence: 99%

“…In addition, based on the improved Leray-Schauder degree, the existence of a solution to problem (1.2) was also considered. Based on Schaefer's fixed point theorem, Elsayed et al 24 proved the existence, uniqueness, and stability results to BVP-FDEs under Hilfer-Katugampola fractional derivative as follows:…”

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confidence: 99%

Hyers–Ulam stability for boundary value problem of fractional differential equations with κ‐Caputo fractional derivative

Rassias

Hoa

2022

Math Methods in App Sciences

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“…Just as differential equations are called continuous dynamical systems, difference equations are called discrete dynamical systems that play a very important role in describing many problems in the real world. For example, when describing continuous variables such as parameter t , where t T  , mathematical models for many practical problems can be established by differential equations (see, e.g., [1][2][3][4][5][6][7][8][9][10][11] and the references therein). However, many variables in the real world are not necessarily continuous in performancewe call them discrete variables-such as number of times, days, and so on.…”

Section: Introductionmentioning

confidence: 99%

“…Definition 6. A point ( , ) x y x y I I   is called an equilibrium point of symmetric system (10) if ( , , , , , , , ) , , , , , y g x x x y y y   …”

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confidence: 99%

Dynamic Behavior of a Fractional-Type Fuzzy Difference System

et al. 2022

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In this paper, our aim is to study the following fuzzy system: xn+1=Axn−1xn−2+Bxn−3D+Cxn−4, n=0,1,2,⋯, where {xn} is a sequence of positive fuzzy numbers and the initial conditions x−4,x−3,x−2,x−1,x0 and the parameters A,B,C,D are positive fuzzy numbers. Firstly, the existence and uniqueness of positive fuzzy solutions of the fuzzy system are proved. Secondly, the dynamic behavior of the equilibrium points for the fuzzy system are studied by means of the fuzzy sets theory, linearization method and mathematical induction. Finally, the results obtained in this paper are simulated by using the software package MATLAB 2016, and the numerical results not only show the dynamic behavior of the solutions for the fuzzy system, but also verify the effectiveness of the proposed results.

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“…There are several kinds of fractional derivatives such as the Riemann-Liouville, Caputo, Hilfer, Hadamard, and others. Recent results on the fractional calculus and fractional differential equations can be found in [4][5][6][7][8][9][10][11][12][13][14]. In [15], by means of Monch's fixed point theorem, Subashini et al consider the existence of mild solutions to a class of evolution equations involving the Hilfer derivative.…”

Section: Introductionmentioning

confidence: 99%

Boundary Value Problem for Fractional Order Generalized Hilfer-Type Fractional Derivative with Non-Instantaneous Impulses

et al. 2020

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This manuscript is devoted to proving some results concerning the existence of solutions to a class of boundary value problems for nonlinear implicit fractional differential equations with non-instantaneous impulses and generalized Hilfer fractional derivatives. The results are based on Banach’s contraction principle and Krasnosel’skii’s fixed point theorem. To illustrate the results, an example is provided.

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On the Existence and Stability of Boundary Value Problem for Differential Equation with Hilfer-Katugampola Fractional Derivative

Cited by 16 publications

References 14 publications

Hyers–Ulam stability for boundary value problem of fractional differential equations with κ‐Caputo fractional derivative

Hyers–Ulam stability for boundary value problem of fractional differential equations with κ‐Caputo fractional derivative

Dynamic Behavior of a Fractional-Type Fuzzy Difference System

Boundary Value Problem for Fractional Order Generalized Hilfer-Type Fractional Derivative with Non-Instantaneous Impulses

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