Analysis of fractional stochastic evolution equations by using Hilfer derivative of finite approximate controllability

Moumen, Abdelkader; Shafqat, Ramsha; Alsinai, Ammar; Boulares, Hamid; Cancan, Murat; Jeelani, Mdi Begum

doi:10.3934/math.2023821

Cited by 15 publications

(4 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[ 30 ] studied measles epidemic model with the constant proportional Caputo operator. Some other useful results using fractional derivatives were presented in [ 31 – 33 ].…”

Section: Introductionmentioning

confidence: 99%

A study of time-fractional model for atmospheric internal waves with Caputo-Fabrizio derivative

Vivas-Cortez,

Sadaf,

Perveen

et al. 2024

PLoS ONE

View full text Add to dashboard Cite

The internal atmospheric waves are gravity waves and occur in the inner part of the fluid system. In this study, a time-fractional model for internal atmospheric waves is investigated with the Caputo-Fabrizio time-fractional differential operator. The analytical solution of the considered model is retrieved by the Elzaki Adomian decomposition method. The variation in the solution is examined for increasing order of the fractional parameter α through numerical and graphical simulations. The accuracy of the obtained results is established by comparing the obtained solution of considered fractional model with the results available in the literature.

show abstract

“…[ 30 ] studied measles epidemic model with the constant proportional Caputo operator. Some other useful results using fractional derivatives were presented in [ 31 – 33 ].…”

Section: Introductionmentioning

confidence: 99%

A study of time-fractional model for atmospheric internal waves with Caputo-Fabrizio derivative

Vivas-Cortez,

Sadaf,

Perveen

et al. 2024

PLoS ONE

View full text Add to dashboard Cite

show abstract

“…In recent times, there has been a growing trend among researchers to explore the practical applications of Ulam-Hyers stability, as evidenced by references ( [26][27][28][29][30][31][32][33]).…”

Section: Introductionmentioning

confidence: 99%

On the Existence and Ulam Stability of BVP within Kernel Fractional Time

Saber,

Imsatfia,

Boulares

et al. 2023

Fractal Fract

Self Cite

View full text Add to dashboard Cite

This manuscript, we establish novel findings regarding the existence of solutions for second-order fractional differential equations employing Ψ-Caputo fractional derivatives. The application of Banach’s fixed-point theorem (BFPT) ensures the uniqueness of the solutions, while Schauder’s fixed-point theorem (SFPT) is instrumental in determining the existence of these solutions. Furthermore, we assess the stability of the proposed equation using the Ulam–Hyers stability criterion. To illustrate our results, we provide a concrete example showcasing their practical implications.

show abstract

“…Abuasbeh et al [28] explored several existence and controllability theories for the Caputo order q ∈ (1, 2) of delay and fractional functional integro-evolution equations (FFIEEs). Moumen et al [29] discussed the approximate controllability of a class of fractional stochastic evolution equations (FSEEs) in the Hilbert space using the Hilfer derivative. However, to the best of our knowledge, the issue of approximate controllability for fractional stochastic differential inclusions with non-local conditions has not yet been examined.…”

Section: Introductionmentioning

confidence: 99%

Approximate Controllability of Fractional Stochastic Evolution Inclusions with Non-Local Conditions

et al. 2023

View full text Add to dashboard Cite

This article investigates the approximate controllability of non-linear fractional stochastic differential inclusions with non-local conditions. We establish a set of sufficient conditions for their approximate controllability and provide results in terms of controllability for the fractional stochastic control system. Our approach relies on using fractional calculus and the fixed-point theorem for multiple-valued operators. Finally, we present an illustrative example to support our findings.

show abstract

Analysis of fractional stochastic evolution equations by using Hilfer derivative of finite approximate controllability

Cited by 15 publications

References 42 publications

A study of time-fractional model for atmospheric internal waves with Caputo-Fabrizio derivative

A study of time-fractional model for atmospheric internal waves with Caputo-Fabrizio derivative

On the Existence and Ulam Stability of BVP within Kernel Fractional Time

Approximate Controllability of Fractional Stochastic Evolution Inclusions with Non-Local Conditions

Contact Info

Product

Resources

About