Controllability of discrete-time semilinear Riemann–Liouville-like fractional equations

Malik, Muslim; Vijayakumar, V.; Shukla, Anurag

doi:10.1016/j.chaos.2023.113959

Cited by 5 publications

(2 citation statements)

References 38 publications

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“…Their application extends across various fields including economics, biology, power systems, chemical process control, electronics, transportation, space technology, engineering, physics, robotics, and chemistry. Extensive research conducted by experts in the field of exact controllability of fractional systems, as indicated by papers such as [13][14][15], highlights the significance of addressing these problems, making them a prominent focus for young academics. In recent times, numerous scholars have engaged in discussions surrounding approximate controllability problems.…”

Section: Introductionmentioning

confidence: 99%

An analysis on the approximate controllability outcomes for fractional stochastic Sobolev‐type hemivariational inequalities of order 1 < r < 2 using sectorial operators

Dineshkumar,

Joo

2024

Math Methods in App Sciences

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In this paper, we deal with the approximate controllability of fractional stochastic Sobolev‐type hemivariational differential systems of order with sectorial operators. Firstly, by using stochastic analysis, fractional calculus, sine and cosine family operators, sectorial operators, and the fixed‐point theorems of multivalued maps, we show the existence of mild solutions for the fractional stochastic evolution systems. Then, we provide a sufficient condition to guarantee the approximate controllability of the stochastic evolution systems. Next, our results cover problems involving nonlocal conditions. Finally, we present theoretical and practical applications to support the validity of the study.

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Section: Introductionmentioning

confidence: 99%

An analysis on the approximate controllability outcomes for fractional stochastic Sobolev‐type hemivariational inequalities of order 1 < r < 2 using sectorial operators

Dineshkumar,

Joo

2024

Math Methods in App Sciences

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“…The long-memory properties of fractional calculus not only reflect local characteristics at the time of evaluation but also reflect the entire history of the function. Therefore, fractional calculus was extensively used in complex nonlinear dynamical systems with memory and genetic properties [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Development of an Efficient Variable Step-Size Gradient Method Utilizing Variable Fractional Derivatives

Ye,

Chen,

Liu

2023

Fractal Fract

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The fractional gradient method has garnered significant attention from researchers. The common view regarding fractional-order gradient methods is that they have a faster convergence rate compared to classical gradient methods. However, through conducting theoretical convergence analysis, we have revealed that the maximum convergence rate of the fractional-order gradient method is the same as that of the classical gradient method. This discovery implies that the superiority of fractional gradients may not reside in achieving fast convergence rates compared to the classical gradient method. Building upon this discovery, a novel variable fractional-type gradient method is proposed with an emphasis on automatically adjusting the step size. Theoretical analysis confirms the convergence of the proposed method. Numerical experiments demonstrate that the proposed method can converge to the extremum point both rapidly and accurately. Additionally, the Armijo criterion is introduced to ensure that the proposed gradient methods, along with various existing gradient methods, can select the optimal step size at each iteration. The results indicate that, despite the proposed method and existing gradient methods having the same theoretical maximum convergence speed, the introduced variable step size mechanism in the proposed method consistently demonstrates superior convergence stability and performance when applied to practical problems.

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Approximate controllability of third order dispersion systems

Gautam,

Shukla,

Johnson

et al. 2024

Bulletin des Sciences Mathématiques

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Controllability of discrete-time semilinear Riemann–Liouville-like fractional equations

Cited by 5 publications

References 38 publications

An analysis on the approximate controllability outcomes for fractional stochastic Sobolev‐type hemivariational inequalities of order 1 < r < 2 using sectorial operators

An analysis on the approximate controllability outcomes for fractional stochastic Sobolev‐type hemivariational inequalities of order 1 < r < 2 using sectorial operators

Development of an Efficient Variable Step-Size Gradient Method Utilizing Variable Fractional Derivatives

Approximate controllability of third order dispersion systems

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