Integro-Differential Boundary Conditions to the Sequential ψ1-Hilfer and ψ2-Caputo Fractional Differential Equations

Sitho, Surang; Ntouyas, Sotiris K.; Sudprasert, Chayapat; Tariboon, Jessada

doi:10.3390/math11040867

Cited by 4 publications

(1 citation statement)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Differential hemivariational inequalities, as well as differential variationalhemivariational inequalities, are important extensions of differential variational inequalities, even though they couple a differential or partial differential equation with a hemivariational inequality and a variational-hemivariational inequality, respectively, where the existence and uniqueness results for various classes of differential variational-hemivariational inequalities have been determined. The references in the field are [6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

The Existence Problems of Solutions for a Class of Differential Variational–Hemivariational Inequality Problems

et al. 2023

View full text Add to dashboard Cite

In this work, we used reflexive Banach spaces to study the differential variational—hemivariational inequality problems with constraints. We established a sequence of perturbed differential variational–hemivariational inequality problems with perturbed constraints and penalty coefficients. Then, for each perturbed inequality, we proved the unique solvability and convergence of the solutions to the problems. Following that, we proposed a mathematical model for a viscoelastic rod in unilateral contact equilibrium, where the unknowns were the displacement field and the history of the deformation. We used the abstract penalty method in the analysis of this inequality and provided the corresponding mechanical interpretations.

show abstract

Section: Introductionmentioning

confidence: 99%

The Existence Problems of Solutions for a Class of Differential Variational–Hemivariational Inequality Problems

et al. 2023

View full text Add to dashboard Cite

show abstract

A Second-Order Accurate Numerical Approximation for a Two-Sided Space-Fractional Diffusion Equation

et al. 2023

View full text Add to dashboard Cite

In this paper, we investigate a practical numerical method for solving a one-dimensional two-sided space-fractional diffusion equation with variable coefficients in a finite domain, which is based on the classical Crank-Nicolson (CN) method combined with Richardson extrapolation. Second-order exact numerical estimates in time and space are obtained. The unconditional stability and convergence of the method are tested. Two numerical examples are also presented and compared with the exact solution.

show abstract

Systems of Sequential ψ1-Hilfer and ψ2-Caputo Fractional Differential Equations with Fractional Integro-Differential Nonlocal Boundary Conditions

et al. 2023

View full text Add to dashboard Cite

In this paper, we introduce and study a new class of coupled and uncoupled systems, consisting of mixed-type ψ1-Hilfer and ψ2-Caputo fractional differential equations supplemented with asymmetric and symmetric integro-differential nonlocal boundary conditions (systems (2) and (13), respectively). As far as we know, this combination of ψ1-Hilfer and ψ2-Caputo fractional derivatives in coupled systems is new in the literature. The uniqueness result is achieved via the Banach contraction mapping principle, while the existence result is established by applying the Leray–Schauder alternative. Numerical examples illustrating the obtained results are also presented.

show abstract

Integro-Differential Boundary Conditions to the Sequential ψ1-Hilfer and ψ2-Caputo Fractional Differential Equations

Cited by 4 publications

References 18 publications

The Existence Problems of Solutions for a Class of Differential Variational–Hemivariational Inequality Problems

The Existence Problems of Solutions for a Class of Differential Variational–Hemivariational Inequality Problems

A Second-Order Accurate Numerical Approximation for a Two-Sided Space-Fractional Diffusion Equation

Systems of Sequential ψ1-Hilfer and ψ2-Caputo Fractional Differential Equations with Fractional Integro-Differential Nonlocal Boundary Conditions

Contact Info

Product

Resources

About