Piecewise continuous solutions of initial value problems of singular fractional differential equations with impulse effects

Liu, Yuji

doi:10.1016/s0252-9602(16)30085-6

Cited by 4 publications

(6 citation statements)

References 28 publications

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“…The first class is impulsive fractional differential equations with multiple starting points see [33]. The second one is impulsive fractional differential equations with a single starting point see [14][15][16].…”

Section: Discussionmentioning

confidence: 99%

“…Substitute d i into (16), we get (14). Now we suppose that x satisfies (14). We will prove that x ∈ X and x is a solution of BVP (1).…”

Section: Lemma 25mentioning

confidence: 99%

“…For examples, impulsive anti-periodic boundary value problems see [4,5,33], impulsive periodic boundary value problems see [17,34], impulsive initial value problems see [30], two-point, threepoint or multi-point impulsive boundary value problems see [37], impulsive boundary value problems on infinite intervals see [38]. Recent studies on solvability of boundary value problems for impulsive fractional differential equations may be seen in [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

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Boundary value problems for impulsive Bagley–Torvik models involving the Riemann–Liouville fractional derivatives

Liu

2016

São Paulo J. Math. Sci.

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By using the Picard iterative technique, we get the exact expression of solutions of linear fractional Bagley-Torvik model. Then the piecewise continuous solutions of this kind of models are obtained. By using these results, we convert the boundary value problems for impulsive fractional differential equations to integral equations technically. By using the weighted function Banach spaces, the completely continuous operators and the Schauder's fixed point theorem, some existence results for solutions of the boundary value problems for impulsive Bagley-Torvik fractional differential equations are established. Examples are given to illustrate the main results.

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Section: Discussionmentioning

confidence: 99%

“…Substitute d i into (16), we get (14). Now we suppose that x satisfies (14). We will prove that x ∈ X and x is a solution of BVP (1).…”

Section: Lemma 25mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Boundary value problems for impulsive Bagley–Torvik models involving the Riemann–Liouville fractional derivatives

Liu

2016

São Paulo J. Math. Sci.

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“…The fractional evolution equation has been applied to many fields, and scholars have obtained abundant research achievements [1][2][3][4][5][6][7][8][9][10][11][12][13]. Impulsive fractional integrodifferential equations can describe some phenomena which often occur in physics, geology, and economics, for instance, earthquake, the closing of the switch in the circuit, and so on.…”

Section: Introductionmentioning

confidence: 99%

“…Impulsive fractional integrodifferential equations can describe some phenomena which often occur in physics, geology, and economics, for instance, earthquake, the closing of the switch in the circuit, and so on. Many scholars are committed to this subject and have achieved plentiful results [1][2][3][4][5][6][7]. Based on the fact that nonlocal initial conditions are more effective than classical initial conditions in applied physics, the study of differential equations with nonlocal conditions has attracted more and more researchers' attention [8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Impulsive Fractional Semilinear Integrodifferential Equations with Nonlocal Conditions

Xue

Zhu

2021

Journal of Function Spaces

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This paper is devoted to a class of impulsive fractional semilinear integrodifferential equations with nonlocal initial conditions. Based on the semigroup theory and some fixed point theorems, the existence theory of PC-mild solutions is established under the condition of compact resolvent operator. Furthermore, the uniqueness of PC-mild solutions is proved in the case of the noncompact resolvent operator.

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On the periodic boundary value problems for fractional nonautonomous differential equations with non-instantaneous impulses

Wang

Zhu

2022

Adv Cont Discr Mod

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In this paper, we investigate periodic boundary value problems for Caputo type fractional semilinear nonautonomous differential equations with non-instantaneous impulses. By using semigroup theory combined with the measure of noncompactness and some fixed point theorems, the existence of PC-mild solutions for the equations is established. At the end, an example is presented to illustrate the application of our main results.

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Piecewise continuous solutions of initial value problems of singular fractional differential equations with impulse effects

Cited by 4 publications

References 28 publications

Boundary value problems for impulsive Bagley–Torvik models involving the Riemann–Liouville fractional derivatives

Boundary value problems for impulsive Bagley–Torvik models involving the Riemann–Liouville fractional derivatives

Impulsive Fractional Semilinear Integrodifferential Equations with Nonlocal Conditions

On the periodic boundary value problems for fractional nonautonomous differential equations with non-instantaneous impulses

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