Non-Instantaneous Impulsive Boundary Value Problems Containing Caputo Fractional Derivative of a Function with Respect to Another Function and Riemann–Stieltjes Fractional Integral Boundary Conditions

Asawasamrit, Suphawat; Thadang, Yasintorn; Ntouyas, Sotiris K.; Tariboon, Jessada

doi:10.3390/axioms10030130

Cited by 13 publications

(10 citation statements)

References 26 publications

(24 reference statements)

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“…There has been a lot of research completed so far on fractional differential equations (FDEs) with initial and boundary conditions (BCs). The reason for this is FDEs accurately describe many real-world phenomena such as biology, physics, chemistry, signal processing, and many more (see, e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13]). Furthermore, it should be remarked that FDEs have interesting applications in solving inverse problems, and in the modeling of heat flow in porous material (see, e.g., [14][15][16][17][18][19][20][21][22][23][24][25]).…”

Section: Introductionmentioning

confidence: 99%

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On Ψ-Hilfer Fractional Integro-Differential Equations with Non-Instantaneous Impulsive Conditions

Arul¹,

Karthikeyan²,

Karthikeyan

et al. 2022

Fractal Fract

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Section: Introductionmentioning

confidence: 99%

“…In [1], S. Asawasamrit et al studied the Ψ-Caputo fractional derivative (FD) and N-InI BVPs. In [28], V. Gupta et al established the FDEs with N-InI.…”

Section: Introductionmentioning

confidence: 99%

On Ψ-Hilfer Fractional Integro-Differential Equations with Non-Instantaneous Impulsive Conditions

Arul¹,

Karthikeyan²,

Karthikeyan

et al. 2022

Fractal Fract

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“…GPU-based modeling is considered with a parallel fractional-order derivative in [11]. The boundary-value problems containing fractional derivatives and fractional integral boundary conditions were considered in [12]. Also, different definitions of fractional derivatives were used in FDEs [13].…”

Section: Introductionmentioning

confidence: 99%

A capable numerical meshless scheme for solving distributed order time-fractional reaction-diffusion equation

Hesameddini

Habibirad

Azin

2022

Preprint

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Distributed order fractional differential equations are efficient in describing physical phenomena because of the differential order distribution. In this paper, the distributed order time-fractional reaction-diffusion equation is considered in the sense of Caputo fractional derivative. A hybrid method is developed based on the Moving Kriging (MK) interpolation and finite difference method for solving this distributed order equation. First, the distributed integral is discretized by the $M$-point Gauss Legendre quadrature rule. Then, the $L2-1_{\sigma}$ method is applied to approximate the solution of the fractional derivative discretization. Also, the unconditionally stability and rate of convergence $O(\tau^{2})$ of the time-discrete technique are illustrated. Furthermore, the MK interpolation is applied in the space variables discretization. Finally, some examples are presented to indicate the efficiency of this method and endorsement the theoretical results.

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“…Several other recent papers include, for instance, [32], where the type of derivative considered was Caputo fractional derivatives with respect to a fixed function, and, under this framework the authors studied an impulsive problem subject to integral boundary conditions based on the Riemann-Stieltjes fractional integral through Leray-Schauder's nonlinear alternative; or [33], where ψ-Caputo operators were considered in the differential equation and in the integral boundary conditions, and the method of upper and lower solutions coupled with the monotone iterative technique were the main tools used.…”

Section: Introductionmentioning

confidence: 99%

Existence of Solutions to a Class of Nonlinear Arbitrary Order Differential Equations Subject to Integral Boundary Conditions

2021

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We investigate the existence of positive solutions for a class of fractional differential equations of arbitrary order δ>2, subject to boundary conditions that include an integral operator of the fractional type. The consideration of this type of boundary conditions allows us to consider heterogeneity on the dependence specified by the restriction added to the equation as a relevant issue for applications. An existence result is obtained for the sublinear and superlinear case by using the Guo–Krasnosel’skii fixed point theorem through the definition of adequate conical shells that allow us to localize the solution. As additional tools in our procedure, we obtain the explicit expression of Green’s function associated to an auxiliary linear fractional boundary value problem, and we study some of its properties, such as the sign and some useful upper and lower estimates. Finally, an example is given to illustrate the results.

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Non-Instantaneous Impulsive Boundary Value Problems Containing Caputo Fractional Derivative of a Function with Respect to Another Function and Riemann–Stieltjes Fractional Integral Boundary Conditions

Cited by 13 publications

References 26 publications

On Ψ-Hilfer Fractional Integro-Differential Equations with Non-Instantaneous Impulsive Conditions

On Ψ-Hilfer Fractional Integro-Differential Equations with Non-Instantaneous Impulsive Conditions

A capable numerical meshless scheme for solving distributed order time-fractional reaction-diffusion equation

Existence of Solutions to a Class of Nonlinear Arbitrary Order Differential Equations Subject to Integral Boundary Conditions

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