Approximate controllability of semilinear fractional differential systems of order 1 &lt; q &lt; 2 via resolvent operators

Lian, Tingting; Fan, Zhenbin; Li, Gang

doi:10.2298/fil1718769l

Cited by 17 publications

(9 citation statements)

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“…The latter for control systems is more crucial since the conditions of former are usually too strong . Many researchers studied the approximate controllability of FDEs; see previous studies and the references therein. However, these works consider the approximate controllability problems only in the Caputo or Riemman‐Liouville's sense.…”

Section: Introductionmentioning

confidence: 99%

Approximate controllability of Hilfer fractional differential equations

Yang

2019

Math Methods in App Sciences

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In this paper, the approximate controllability for a class of Hilfer fractional differential equations (FDEs) of order 1 < < 2 and type 0 ≤ ≤ 1 is considered.The existence and uniqueness of mild solutions for these equations are established by applying the Banach contraction principle. Further, we obtain a set of sufficient conditions for the approximate controllability of these equations.Finally, an example is presented to illustrate the obtained results. KEYWORDSapproximate controllability, fractional differential equations, Hilfer fractional derivative MSC CLASSIFICATION26A33; 34A08; 35R11; 93B05 k=0 (−z) k k!Γ(1− − k) is defined only when ∈ (0, 1). There are only few papers that deal with the FDEs of order 1 < < 2. By using sectorial operator and -resolvent family, Shu and Wang 16 investigated the existence of mild solutions for Caputo FDEs of order ∈ (1, 2). Li et al. 17 concerned the Cauchy problems for Riemann-Liouville FDEs of order ∈ (1, 2). Li et al. 18 researched the Caputo FDEs of order ∈ (1, 2). To the best of our knowledge, there is no results about Hilfer FDEs of order 1 < < 2 and type 0 ≤ ≤ 1.Math Meth Appl Sci. 2020;43:242-254. wileyonlinelibrary.com/journal/mma

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Section: Introductionmentioning

confidence: 99%

Approximate controllability of Hilfer fractional differential equations

Yang

2019

Math Methods in App Sciences

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“…In recent decades, the fractional differential equations have been applied to various fields successfully, for example, physics, engineering, finance and so on. Consequently, more and more researchers pay much attention to this subject and have obtained substantial achievements, we refer the read to see (Debbouchea and Baleanu 2011;Lian et al 2017;Chang et al 2017;Shu and Shi 2016;Yang et al 2017;Shu et al 2011;Xu et al 2020;Chen et al 2015Chen et al , 2020aKilbas et al 2006) and the references therein.…”

Section: Introductionmentioning

confidence: 99%

A study on impulsive fractional hybrid evolution equations using sequence method

Gou

2020

Comp. Appl. Math.

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In this paper, we introduce a new concept called α-order cosine-resolvent family, by using the theory of fractional calculus, the concepts of measure of noncompactness and Hybrid fixed point theorem, we consider the existence of PC-mild solutions for a class of impulsive fractional hybrid evolution equation in a Banach space. Furthermore, we obtain some sufficient conditions for approximate controllability of our concern problem. At the end, an example is given to illustrate the feasibility of our results.

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“…However, some authors used the idea of analytic sectorial operators to overcome this problem. For more details, we refer the reader to the papers [20][21][22][23] and references therein. To the best of our knowledge, there is not any investigation in the controllability problem via resolvent operators applied on hybrid systems such as the system that has been discussed in the article [24].…”

Section: Introductionmentioning

confidence: 99%