Existence and Stability Results for a Fractional Order Differential Equation with Non-Conjugate Riemann-Stieltjes Integro-Multipoint Boundary Conditions

Ahmad, Bashir; Alruwaily, Ymnah; Alsaedi, Ahmed; Ntouyas, Sotiris K.

doi:10.3390/math7030249

Cited by 14 publications

(14 citation statements)

References 26 publications

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“…where K := sup t∈[0,1] | f (t, 0)| and Λ 1 and Λ 2 are given by (8). Clearly, B r is a closed, bounded, convex and nonempty subset of Banach space E. We consider the operator T : E → E as (7).…”

Section: Resultsmentioning

confidence: 99%

“…Then, the fractional q-integro-difference Equation (1) with q-integral boundary conditions (2) has a unique solution on [0, 1], provided that Λ 0 + LΛ 1 + MΛ 2 < 1, where Λ 0 , Λ 1 , Λ 2 are defined by (8).…”

Section: Resultsmentioning

confidence: 99%

“…and a variety of boundary conditions. For some recent works on the topic, for instance, see [1][2][3][4][5][6][7][8] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

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Existence Theory for a Fractional q-Integro-Difference Equation with q-Integral Boundary Conditions of Different Orders

2019

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In this paper, we study the existence of solutions for a new class of fractional q-integro-difference equations involving Riemann-Liouville q-derivatives and a q-integral of different orders, supplemented with boundary conditions containing q-integrals of different orders. The first existence result is obtained by means of Krasnoselskii's fixed point theorem, while the second one relies on a Leray-Schauder nonlinear alternative. The uniqueness result is derived via the Banach contraction mapping principle. Finally, illustrative examples are presented to show the validity of the obtained results. The paper concludes with some interesting observations. Keywords: q-integro-difference equation; boundary value problem; existence; fixed pointwhere f ∈ C([0, 1] × R, R), c D α q is the fractional q-derivative of the Caputo type, and α i , β i , γ i , η i ∈ R, i = 1, 2.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

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Existence Theory for a Fractional q-Integro-Difference Equation with q-Integral Boundary Conditions of Different Orders

2019

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“…The problems of membrane structure are generally shown as large deflection problems, which makes it inevitable to produce nonlinear differential equations in solving. Generally, these nonlinear differential equations will bring serious analytical difficulties even in simple boundary-value problems [7][8][9][10][11][12][13][14][15][16][17]. Thus, the closed-form solutions of these membrane problems are usually difficult to be obtained.…”

Section: Introductionmentioning

confidence: 99%

A Closed-Form Solution of Prestressed Annular Membrane Internally-Connected with Rigid Circular Plate and Transversely-Loaded by Central Shaft

et al. 2020

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In this paper, we analytically dealt with the usually so-called prestressed annular membrane problem, that is, the problem of axisymmetric deformation of the annular membrane with an initial in-plane tensile stress, in which the prestressed annular membrane is peripherally fixed, internally connected with a rigid circular plate, and loaded by a shaft at the center of this rigid circular plate. The prestress effect, that is, the influence of the initial stress in the undeformed membrane on the axisymmetric deformation of the membrane, was taken into account in this study by establishing the boundary condition with initial stress, while in the existing work by establishing the physical equation with initial stress. By creating an integral expression of elementary function, the governing equation of a second-order differential equation was reduced to a first-order differential equation with an undetermined integral constant. According to the three preconditions that the undetermined integral constant is less than, equal to, or greater than zero, the resulting first-order differential equation was further divided into three cases to solve, such that each case can be solved by creating a new integral expression of elementary function. Finally, a characteristic equation for determining the three preconditions was deduced in order to make the three preconditions correspond to the situation in practice. The solution presented here could be called the extended annular membrane solution since it can be regressed into the classic annular membrane solution when the initial stress is equal to zero.

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“…, n -2 and A is a function of bounded variation. In passing we remark that the present work is motivated by a recent paper [23], where the authors studied the existence and stability of solutions for a fractional-order differential equation with non-conjugate Riemann-Stieltjes integro-multipoint boundary conditions. We arrange the rest of the paper as follows.…”

Section: Introductionmentioning

confidence: 99%

On a coupled system of higher order nonlinear Caputo fractional differential equations with coupled Riemann–Stieltjes type integro-multipoint boundary conditions

et al. 2019

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We study a coupled system of Caputo fractional differential equations with coupled non-conjugate Riemann-Stieltjes type integro-multipoint boundary conditions. Existence and uniqueness results for the given boundary value problem are obtained by applying the Leray-Schauder nonlinear alternative, the Krasnoselskii fixed point theorem and Banach's contraction mapping principle. Examples are constructed to illustrate the obtained results.

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Existence and Stability Results for a Fractional Order Differential Equation with Non-Conjugate Riemann-Stieltjes Integro-Multipoint Boundary Conditions

Cited by 14 publications

References 26 publications

Existence Theory for a Fractional q-Integro-Difference Equation with q-Integral Boundary Conditions of Different Orders

Existence Theory for a Fractional q-Integro-Difference Equation with q-Integral Boundary Conditions of Different Orders

A Closed-Form Solution of Prestressed Annular Membrane Internally-Connected with Rigid Circular Plate and Transversely-Loaded by Central Shaft

On a coupled system of higher order nonlinear Caputo fractional differential equations with coupled Riemann–Stieltjes type integro-multipoint boundary conditions

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