Existence and Stability of Solutions to Neutral Conformable Stochastic Functional Differential Equations

Xiao, Guanli; Wang, JinRong; O’Regan, Donal

doi:10.1007/s12346-021-00538-x

Cited by 5 publications

(1 citation statement)

References 33 publications

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“…The above papers concern research on integer order derivative, while the works of conformable type derivative are very few ( [15][16][17][18][19][20]). The conformable derivative not only has some properties of fractional derivative, but also some properties of integer order derivatives.…”

Section: Introductionmentioning

confidence: 99%

g-Expectation for Conformable Backward Stochastic Differential Equations

Luo

Fečkan

Wang

et al. 2022

Axioms

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In this paper, we study the applications of conformable backward stochastic differential equations driven by Brownian motion and compensated random measure in nonlinear expectation. From the comparison theorem, we introduce the concept of g-expectation and give related properties of g-expectation. In addition, we find that the properties of conformable backward stochastic differential equations can be deduced from the properties of the generator g. Finally, we extend the nonlinear Doob–Meyer decomposition theorem to more general cases.

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Section: Introductionmentioning

confidence: 99%

g-Expectation for Conformable Backward Stochastic Differential Equations

Luo

Fečkan

Wang

et al. 2022

Axioms

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show abstract

Exponential stability of impulsive conformable fractional-order nonlinear differential system with time-varying delay and its applications

Xiao,

2023

Neurocomputing

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On the Solvability of Iterative Systems of Fractional-Order Differential Equations with Parameterized Integral Boundary Conditions

BODDU,

KHUDDUSH

2024

Universal Journal of Mathematics and Applications

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The aim of this paper is to determine the eigenvalue intervals of µk, 1 ≤ k ≤ n for which an iterative systems of a class of fractional-order differential equations with parameterized integral boundary conditions (BCs) has at least one positive solution by means of standard fixed point theorem of cone type. To the best of our knowledge, this will be the first time that we attempt to reach such findings for the topic at hand in the literature. The obtained results in the paper are illustrated with an example for their feasibility.

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Existence and Stability of Solutions to Neutral Conformable Stochastic Functional Differential Equations

Cited by 5 publications

References 33 publications

g-Expectation for Conformable Backward Stochastic Differential Equations

g-Expectation for Conformable Backward Stochastic Differential Equations

Exponential stability of impulsive conformable fractional-order nonlinear differential system with time-varying delay and its applications

On the Solvability of Iterative Systems of Fractional-Order Differential Equations with Parameterized Integral Boundary Conditions

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