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Search Results (4)

Search Parameters:
Keywords = Hilfer fractional (HF) system

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22 pages, 436 KiB  
Article
Existence of Sobolev-Type Hilfer Fractional Neutral Stochastic Evolution Hemivariational Inequalities and Optimal Controls
by Sivajiganesan Sivasankar, Ramalingam Udhayakumar, Venkatesan Muthukumaran, Saradha Madhrubootham, Ghada AlNemer and Ahmed M. Elshenhab
Fractal Fract. 2023, 7(4), 303; https://doi.org/10.3390/fractalfract7040303 - 30 Mar 2023
Cited by 7 | Viewed by 2114
Abstract
This article concentrates on a control system with a nonlocal condition that is driven by neutral stochastic evolution hemivariational inequalities (HVIs) of Sobolev-type Hilfer fractional (HF). In order to illustrate the necessary requirements for the existence of mild solutions to the required control [...] Read more.
This article concentrates on a control system with a nonlocal condition that is driven by neutral stochastic evolution hemivariational inequalities (HVIs) of Sobolev-type Hilfer fractional (HF). In order to illustrate the necessary requirements for the existence of mild solutions to the required control system, we first use the characteristics of the modified Clarke sub-differential and a fixed point approach for multivalued functions. Then, we show that there are optimal state-control sets that are driven by Sobolev-type HF neutral stochastic evolution HVIs utilizing constrained Lagrange optimal systems. The optimal control (OC) results are created without taking the uniqueness of the control system solutions into account. Finally, the main finding is shown by an example. Full article
(This article belongs to the Special Issue Recent Advances in Fractional Differential Equations and Their Applications)
18 pages, 354 KiB  
Article
Existence of Hilfer Fractional Stochastic Differential Equations with Nonlocal Conditions and Delay via Almost Sectorial Operators
by Sivajiganesan Sivasankar, Ramalingam Udhayakumar, Velmurugan Subramanian, Ghada AlNemer and Ahmed M. Elshenhab
Mathematics 2022, 10(22), 4392; https://doi.org/10.3390/math10224392 - 21 Nov 2022
Cited by 8 | Viewed by 2147
Abstract
In this article, we examine the existence of Hilfer fractional (HF) stochastic differential systems with nonlocal conditions and delay via almost sectorial operators. The major methods depend on the semigroup of operators method and the Mo¨nch [...] Read more.
In this article, we examine the existence of Hilfer fractional (HF) stochastic differential systems with nonlocal conditions and delay via almost sectorial operators. The major methods depend on the semigroup of operators method and the Mo¨nch fixed-point technique via the measure of noncompactness, and the fundamental theory of fractional calculus. Finally, to clarify our key points, we provide an application. Full article
(This article belongs to the Special Issue Fractional Calculus and Nonlinear Systems)
16 pages, 340 KiB  
Article
New Outcomes Regarding the Existence of Hilfer Fractional Stochastic Differential Systems via Almost Sectorial Operators
by Sivajiganesan Sivasankar and Ramalingam Udhayakumar
Fractal Fract. 2022, 6(9), 522; https://doi.org/10.3390/fractalfract6090522 - 16 Sep 2022
Cited by 13 | Viewed by 1629
Abstract
In this paper, we focus on the existence of Hilfer fractional stochastic differential systems via almost sectorial operators. The main results are obtained by using the concepts and ideas from fractional calculus, multivalued maps, semigroup theory, sectorial operators, and the fixed-point technique. We [...] Read more.
In this paper, we focus on the existence of Hilfer fractional stochastic differential systems via almost sectorial operators. The main results are obtained by using the concepts and ideas from fractional calculus, multivalued maps, semigroup theory, sectorial operators, and the fixed-point technique. We start by confirming the existence of the mild solution by using Dhage’s fixed-point theorem. Finally, an example is provided to demonstrate the considered Hilferr fractional stochastic differential systems theory. Full article
(This article belongs to the Special Issue Finite Difference Methods for Fractional and Stochastic Differential Equations)
19 pages, 348 KiB  
Article
Hilfer Fractional Neutral Stochastic Volterra Integro-Differential Inclusions via Almost Sectorial Operators
by Sivajiganesan Sivasankar and Ramalingam Udhayakumar
Mathematics 2022, 10(12), 2074; https://doi.org/10.3390/math10122074 - 15 Jun 2022
Cited by 22 | Viewed by 1914
Abstract
In our paper, we mainly concentrate on the existence of Hilfer fractional neutral stochastic Volterra integro-differential inclusions with almost sectorial operators. The facts related to fractional calculus, stochastic analysis theory, and the fixed point theorem for multivalued maps are used to prove the [...] Read more.
In our paper, we mainly concentrate on the existence of Hilfer fractional neutral stochastic Volterra integro-differential inclusions with almost sectorial operators. The facts related to fractional calculus, stochastic analysis theory, and the fixed point theorem for multivalued maps are used to prove the result. In addition, an illustration of the principle is provided. Full article
(This article belongs to the Special Issue Advances in Differential and Difference Equations with Applications 2023)
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