Existence of solutions for weighted p(t)-Laplacian mixed Caputo fractional differential equations at resonance

Lakoud, Assia Guezane; Ashyralyev, Allaberen

doi:10.2298/fil2201231g

Cited by 4 publications

(1 citation statement)

References 26 publications

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“…Recent research include fractional calculus in viscoelasticity [1], fractional multidimensional diffusion equations with exponential memory [2], and fractional model of guava for biological pest control with memory effect [3]. Additionally, most recent works include a fractional model of phytoplankton-toxic phytoplankton-zooplankton system [4] and existence of solutions for weighted p(t)-Laplacian mixed Caputo fractional differential equations at resonance [5].…”

Section: Introductionmentioning

confidence: 99%

Bivariate modified Bernstein–Kantorovich operators for the numerical solution of two‐dimensional fractional Volterra integral equations

Buranay

2023

Math Methods in App Sciences

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A class of two‐dimensional fractional Volterra integral equations (2D‐FVIEs) of the second kind is considered. The solution may have unbounded derivatives near the integral domain boundary. Therefore, smoothing transformations are employed to change the original 2D‐FVIEs into new transformed 2D‐FVIEs with better regularity. The novelty in this research concerns both the theoretical investigation of the bivariate modified Bernstein–Kantorovich (B‐MBK) operators and the numerical application of these operators for approximating the unknown solution of 2D‐FVIEs. In this regard, an algorithm is given utilizing the B‐MBK operators and discretization that approximates the solution of the transformed discretized equation. Further, an inverse transformation is applied to obtain the solution of the original equation. Additionally, we illustrate the applicability of the proposed method on examples from the literature.

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Section: Introductionmentioning

confidence: 99%

Bivariate modified Bernstein–Kantorovich operators for the numerical solution of two‐dimensional fractional Volterra integral equations

Buranay

2023

Math Methods in App Sciences

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ON ITERATIVE POSITIVE SOLUTIONS FOR A CLASS OF SINGULAR INFINITE-POINT <i>P</i>-LAPLACIAN FRACTIONAL DIFFERENTIAL EQUATION WITH SINGULAR SOURCE TERMS

Guo¹,

Wang²,

Liu³

et al. 2023

jaac

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Existence of the solution for hybrid differential equation with Caputo-Fabrizio fractional derivative

Chefnaj

Hilal

Kajouni

2023

Filomat

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In this manuscript, we are interested in the existence result of the solution of hybrid nonlinear differential equations. involving fractional Caputo Fabrizio derivatives of arbitrary order ? ?]0, 1[. By applying Dhage?s fixed point theorem and some fractional analysis techniques, we prove our main result. As an application, A non-trivial example is given to demonstrate the effectiveness of our theoretical result.

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Existence of solutions for weighted p(t)-Laplacian mixed Caputo fractional differential equations at resonance

Abstract: Using Mawhin?s coincidence degree theory, we investigate the existence of solutions for a class of weighted p(t)-Laplacian boundary value problems at resonance and involving left and right Caputo fractional derivatives. An example is provided to illustrate the main existence results.

Cited by 4 publications

References 26 publications

Bivariate modified Bernstein–Kantorovich operators for the numerical solution of two‐dimensional fractional Volterra integral equations

Bivariate modified Bernstein–Kantorovich operators for the numerical solution of two‐dimensional fractional Volterra integral equations

ON ITERATIVE POSITIVE SOLUTIONS FOR A CLASS OF SINGULAR INFINITE-POINT <i>P</i>-LAPLACIAN FRACTIONAL DIFFERENTIAL EQUATION WITH SINGULAR SOURCE TERMS

Existence of the solution for hybrid differential equation with Caputo-Fabrizio fractional derivative

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