Analysis of a Nonlinear ψ-Hilfer Fractional Integro-Differential Equation Describing Cantilever Beam Model with Nonlinear Boundary Conditions

Kotsamran, Kanoktip; Sudsutad, Weerawat; Thaiprayoon, Chatthai; Kongson, Jutarat; Alzabut, Jehad

doi:10.3390/fractalfract5040177

Cited by 6 publications

(1 citation statement)

References 40 publications

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“…In [27], the authors established sufficient conditions to approve the existence and uniqueness of solutions of a nonlinear implicit ψ-Hilfer fractional boundary value problem of the cantilever beam model with nonlinear boundary conditions…”

Section: Introductionmentioning

confidence: 99%

Existence and stability results for a sequential $ψ$-Hilfer fractional integro-differential equations with nonlocal boundary conditions

Haddouchi¹

2023

Preprint

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This paper deals with the existence and uniqueness of solutions for a nonlinear boundary value problem involving a sequential ψ-Hilfer fractional integro-differential equations with nonlocal boundary conditions. The existence and uniqueness of solutions are established for the considered problem by using the Banach contraction principle, Sadovski's fixed point theorem, and Krasnoselskii-Schaefer fixed point theorem due to Burton and Kirk. In addition, the Ulam-Hyers stability of solutions is discussed. Finally, the obtained results are illustrated by examples. φ j ,ρ;ψ a +x(ς j ) = G(ξ , x(ξ )),

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Section: Introductionmentioning

confidence: 99%

Existence and stability results for a sequential $ψ$-Hilfer fractional integro-differential equations with nonlocal boundary conditions

Haddouchi¹

2023

Preprint

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Study of a sequential $$\psi $$-Hilfer fractional integro-differential equations with nonlocal BCs

Haddouchi,

Samei,

Rezapour

2023

J. Pseudo-Differ. Oper. Appl.

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Analysis of a Fractional Variational Problem Associated with Cantilever Beams Subjected to a Uniformly Distributed Load

et al. 2023

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In this paper, we investigate the existence and uniqueness of minimizers of a fractional variational problem generalized from the energy functional associated with a cantilever beam under a uniformly distributed load. We apply the fractional Euler–Lagrange condition to formulate the minimization problem as a boundary value problem and obtain existence and uniqueness results in both L2 and L∞ settings. Additionally, we characterize the continuous dependence of the minimizers on varying loads in the energy functional. Moreover, an approximate solution is derived via the homotopy perturbation method, which is numerically demonstrated in various examples. The results show that the deformations are larger for smaller orders of the fractional derivative.

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Analysis of a Nonlinear ψ-Hilfer Fractional Integro-Differential Equation Describing Cantilever Beam Model with Nonlinear Boundary Conditions

Cited by 6 publications

References 40 publications

Existence and stability results for a sequential $ψ$-Hilfer fractional integro-differential equations with nonlocal boundary conditions

Existence and stability results for a sequential $ψ$-Hilfer fractional integro-differential equations with nonlocal boundary conditions

Study of a sequential $$\psi $$-Hilfer fractional integro-differential equations with nonlocal BCs

Analysis of a Fractional Variational Problem Associated with Cantilever Beams Subjected to a Uniformly Distributed Load

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