Hilfer Fractional Differential Equations with Almost Sectorial Operators

Jaiswal, Anjali; Bahuguna, D.

doi:10.1007/s12591-020-00514-y

Cited by 36 publications

(28 citation statements)

References 23 publications

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“…Lemma 3 (See [15]). The operators R α (t) and S α,γ (t) are bounded linear operators on Y for every fixed t ∈ S 0 π 2 −ω .…”

Section: Hypothesis 4 (H4)mentioning

confidence: 99%

“…These short-term perturbations are often treated in the form of impulses. Recently, in many published works, Hilfer fractional differential equations have received attention [8][9][10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

“…In [15], Jaiswal and Bahuguna studied equations of Hilfer fractional derivatives with almost sectorial operators in the abstract sense:…”

Section: Introductionmentioning

confidence: 99%

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Analysis of Hilfer Fractional Integro-Differential Equations with Almost Sectorial Operators

2021

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In this work, we investigate a class of nonlocal integro-differential equations involving Hilfer fractional derivatives and almost sectorial operators. We prove our results by applying Schauder’s fixed point technique. Moreover, we show the fundamental properties of the representation of the solution by discussing two cases related to the associated semigroup. For that, we consider compactness and noncompactness properties, respectively. Furthermore, an example is given to illustrate the obtained theory.

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“…Lemma 3 (See [15]). The operators R α (t) and S α,γ (t) are bounded linear operators on Y for every fixed t ∈ S 0 π 2 −ω .…”

Section: Hypothesis 4 (H4)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analysis of Hilfer Fractional Integro-Differential Equations with Almost Sectorial Operators

2021

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“…There are numerous works focussing on the existence of mild solutions and analytical solutions of fractional evolution equations with almost sectorial operators [16,33,43]. Recently, Jaiswal et al [21] proved the existence of mild solutions of Hilfer FDEs with almost sectorial operators. We found that in the available literature, approximate controllability of Hilfer FDEs with almost sectorial operators has not been discussed yet.…”

Section: Introductionmentioning

confidence: 99%

Existence and approximate controllability of Hilfer fractional evolution equations with almost sectorial operators

et al. 2020

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In this article, we are concerned with the existence of mild solutions and approximate controllability of Hilfer fractional evolution equations with almost sectorial operators and nonlocal conditions. The existence results are obtained by first defining Green’s function and approximate controllability by specifying a suitable control function. These results are established with the help of Schauder’s fixed point theorem and theory of almost sectorial operators in a Banach space. An example is also presented for the demonstration of obtained results.

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“…So, a large number of scientific papers have been devoted to the investigation of initial, boundary, and inverse value problems for linear and nonlinear ordinary and partial differential equations (see also [17][18][19][20][21][22][23][24][25][26]).…”

Section: Introductionmentioning

confidence: 99%

Boundary Value Problem for Weak Nonlinear Partial Differential Equations of Mixed Type with Fractional Hilfer Operator

Yuldashev

Kadirkulov

2020

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In this paper, we consider a boundary value problem for a nonlinear partial differential equation of mixed type with Hilfer operator of fractional integro-differentiation in a positive rectangular domain and with spectral parameter in a negative rectangular domain. With respect to the first variable, this equation is a nonlinear fractional differential equation in the positive part of the considering segment and is a second-order nonlinear differential equation with spectral parameter in the negative part of this segment. Using the Fourier series method, the solutions of nonlinear boundary value problems are constructed in the form of a Fourier series. Theorems on the existence and uniqueness of the classical solution of the problem are proved for regular values of the spectral parameter. For irregular values of the spectral parameter, an infinite number of solutions of the mixed equation in the form of a Fourier series are constructed.

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Hilfer Fractional Differential Equations with Almost Sectorial Operators

Cited by 36 publications

References 23 publications

Analysis of Hilfer Fractional Integro-Differential Equations with Almost Sectorial Operators

Analysis of Hilfer Fractional Integro-Differential Equations with Almost Sectorial Operators

Existence and approximate controllability of Hilfer fractional evolution equations with almost sectorial operators

Boundary Value Problem for Weak Nonlinear Partial Differential Equations of Mixed Type with Fractional Hilfer Operator

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