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Some new dynamic Gronwall–Bellman–Pachpatte type inequalities with delay on time scales and certain applications
The main objective of the present article is to prove some new delay nonlinear dynamic inequalities of Gronwall–Bellman–Pachpatte type on time...
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A Generalized Gronwall-Bellman Inequality
Under study is the integral inequality that has as kernel a nonnegative polynomial in the powers of the difference of arguments and a large parameter N ...
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A new class of nonlinear Gronwall–Bellman delay integral inequalities with power and its applications
In this paper, we establish some new delay Gronwall–Bellman integral inequalities with power, which can be used as a convenient tool to study the...
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Estimation of unknown function of nonlinear weakly singular integral inequalities of Gronwall–Bellman–Pachpatte type
Some new nonlinear weakly singular integral inequalities of Gronwall–Bellman–Pachpatte type are given. The estimations of unknown functions are...
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Asymptotical stabilization of fuzzy semilinear dynamic systems involving the generalized Caputo fractional derivative for \(q \in (1,2)\)
In this study, the asymptotical stabilization problem of fuzzy fractional dynamic systems (FFDSs) with the semilinear form under the granular Caputo...
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A discrete Gronwall–Halanay-type inequality with infinite delay and its applications to difference equations
We establish a discrete Gronwall–Halanay-type inequality with infinite delay, which is not covered in the existing literature. As an application, a...
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A class of backward stochastic Bellman–Bihari’s inequality and its applications
In this paper, we propose and prove several different forms of backward stochastic Bellman–Bihari’s inequality. Then, as two applications, two...
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Existence and data dependence results for fractional differential equations involving atangana-baleanu derivative
In the current paper, we consider multi-derivative nonlinear fractional differential equations involving Atangana-Baleanu fractional derivative. We...
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Convergence to logarithmic-type functions of solutions of fractional systems with Caputo-Hadamard and Hadamard fractional derivatives
As a follow-up to the inherent nature of Caputo-Hadamard fractional derivative ( CHFD ) and the Hadamard fractional derivative ( HFD ), little is known...
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AsymptotIc Behavior of Solutions of Fractional Differential Equations with Hadamard Fractional Derivatives
The asymptotic behaviour of solutions in an appropriate space is discussed for a fractional problem involving Hadamard left-sided fractional...
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A Fractional Bihari Inequality and Some Applications to Fractional Differential Equations and Stochastic Equations
The purpose of this paper is to present a new version of the Bihari inequality with singular kernel and give a simple proof of the fractional...
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Results for Retarded Nonlinear Integral Inequalities with Mixed Powers and Their Applications to Delay Integrodifferential Equations
We present new retarded nonlinear integral inequalities with mixed powers. The obtained inequalities can be used to study the property of boundedness...
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Asymptotic Behavior of the Solutions of Stochastic Functional-Differential Equations
We study the asymptotic behavior at infinity of the solutions of stochastic functional-differential equations by the method of asymptotic equivalence...
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Estimates of Exponential Convergence for Solutions of Stochastic Nonlinear Systems
This paper aims to analyze the behavior of the solutions of a stochastic perturbed system with respect to the solutions of the stochastic unperturbed...
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Trotter-Kato Approximations of Stochastic Differential Equations
The objective of this chapter is to study Trotter-Kato approximations of many classes of stochastic differential equations, including equations with...
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Study of the Asymptotic Properties of the Solution to a Problem with a Parameter for the Sturm–Liouville Operator with a Singular Potential
AbstractThe Sturm–Liouville operator with a singular potential is defined on an interval of the real line. Transmission conditions are specified at...
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The Myshkis 3/2 Theorem and Its Generalizations
We discuss the well-known Myshkis result on the stability of nonautonomous first-order delay differential equations, providing an extension to the...
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Optimal Control Problem for a Hyperbolic System with Delay on the Boundary in the Class of Smooth Controls
In this paper, we examine the optimal control problem for a hyperbolic system with differential constraints on the boundary, taking into account the...
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Applications to Stochastic Stability
In this chapter, we present applications of some of the Trotter-Kato approximation results from Chapter 3 to stochastic stability problems.