On the new fractional configurations of integro-differential Langevin boundary value problems

Rezapour, Shahram; Ahmad, Bashir; Etemad, Sina

doi:10.1016/j.aej.2021.03.070

Cited by 10 publications

(3 citation statements)

References 28 publications

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“…William and Vijayakumar [27] explored the existence of the mild solution for the Atangana-Baleanu neutral impulsive differential system using Darbo fixed point theorem. For more details on it, readers refer to [25,[28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

New exploration on approximate controllability of fractional neutral‐type delay stochastic differential inclusions with non‐instantaneous impulse

Kumar Sharma,

Vats,

Kumar

2024

Math Methods in App Sciences

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This paper aims to derive a new set of sufficient conditions for the existence and approximate controllability of neutral‐type fractional stochastic integrodifferential inclusions with infinite delay and non‐instantaneous impulse in a separable Hilbert space using the Atangana–Baleanu Caputo fractional derivative. We investigate the existence of a mild solution for the Atangana–Baleanu Caputo fractional neutral‐type delay integrodifferential stochastic system while taking into account the non‐instantaneous impulses. For this purpose, the Atangana–Baleanu Caputo fractional neutral‐type impulsive delay stochastic system is transferred into an equivalent fixed point problem via an integral operator, and then, the Bohnenblust–Karlin fixed point approach is applied. Further, the approximate controllability results of the proposed nonlinear stochastic impulsive control system are established under the consideration that the corresponding linear system is approximately controllable. The set of sufficient conditions is established by using the concepts of stochastic analysis, fractional calculus, fixed point technique, semigroup theory of bounded linear operators, and the theory of multivalued maps. To illustrate the abstract results, we provide an example at the end of the paper.

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Section: Introductionmentioning

confidence: 99%

New exploration on approximate controllability of fractional neutral‐type delay stochastic differential inclusions with non‐instantaneous impulse

Kumar Sharma,

Vats,

Kumar

2024

Math Methods in App Sciences

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“…Consequently, fractional calculus got incredible interest and received more attention from many specialists and researchers. It also set up a better sketch over hereditary properties of processes and various materials, consequently many monographs and research papers have been reported in this field [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

An analysis on the controllability and stability to some fractional delay dynamical systems on time scales with impulsive effects

et al. 2021

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In this article, we establish a new class of mixed integral fractional delay dynamic systems with impulsive effects on time scales. We investigate the qualitative properties of the considered systems. In fact, the article contains three segments, and the first segment is devoted to investigating the existence and uniqueness results. In the second segment, we study the stability analysis, while the third segment is devoted to investigating the controllability criterion. We use the Leray–Schauder and Banach fixed point theorems to prove our results. Moreover, the obtained results are examined with the help of an example.

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“…The fractional calculus has been extended extremely and investigated in distinct areas and applications by many research works (see, for example, [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]). In 1937, Fisher, Kolmogorov, Petrovsky, and Piscounov investigated independently the Fisher-KPP equation (or Fisher's equation; see [21,22]).…”

Section: Introductionmentioning

confidence: 99%

Solving partial fractional differential equations by using the Laguerre wavelet-Adomian method

Aghazadeh¹,

Mohammadi²,

Ahmadnezhad³

et al. 2021

Adv Differ Equ

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By using a nonlinear method, we try to solve partial fractional differential equations. In this way, we construct the Laguerre wavelets operational matrix of fractional integration. The method is proposed by utilizing Laguerre wavelets in conjunction with the Adomian decomposition method. We present the procedure of implementation and convergence analysis for the method. This method is tested on fractional Fisher’s equation and the singular fractional Emden–Fowler equation. We compare the results produced by the present method with some well-known results.

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On the new fractional configurations of integro-differential Langevin boundary value problems

Cited by 10 publications

References 28 publications

New exploration on approximate controllability of fractional neutral‐type delay stochastic differential inclusions with non‐instantaneous impulse

New exploration on approximate controllability of fractional neutral‐type delay stochastic differential inclusions with non‐instantaneous impulse

An analysis on the controllability and stability to some fractional delay dynamical systems on time scales with impulsive effects

Solving partial fractional differential equations by using the Laguerre wavelet-Adomian method

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