Existence of solution to a periodic boundary value problem for a nonlinear impulsive fractional differential equation

Belmekki, Mohammed; Nieto, Juan J.; Rodríguez‐López, Rosana

doi:10.14232/ejqtde.2014.1.16

Cited by 19 publications

(16 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Both p and q maybe singular at t = 0, t 1 , t 2 . The impulse functions in this paper are different from those ones in known paper [18,22].…”

Section: Introductionmentioning

confidence: 66%

“…The existence and uniqueness of solutions of BVP (1) are established under some assumptions by using Banach contraction principle. One of the main assumptions in [18] is as follows: In recent paper [22], the following periodic boundary value problem of impulsive fractional differential equation with multiple base points…”

Section: Introductionmentioning

confidence: 99%

“…So the problem we are concerned is a new one. In [1,18,22], the assumptions imposed on the nonlinearities are (A), (B) and (C). But in this paper the assumptions imposed on f, g in (4) involving sup-multiplicative-like functions which do not satisfy (A), (B) and (C) (see Definition 2.6).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

New results on the existence of solutions of boundary value problems for singular fractional differential systems with impulse effects

Liu

2015

Tbilisi Math. J.

View full text Add to dashboard Cite

Results on the existence of solutions to a new class of impulsive singular fractional differential systems with multiple base points are established. The assumptions imposed on the nonlinearities, see ((C) and (D) in Theorem 3.1), are weaker than known ones, (i.e., (A) in Introduction section). The analysis relies on the well known fixed point theorems. An example is given to illustrate the efficiency of the main theorems. The investigation shows that these results and methods are helpful for study in the nonlinear area and the numerical simulation, especially for study in the the numerical solution of a fractional differential equation with multiple base points with or without impulse effects. A section "Conclusions" is given with future work research directions.2010 Mathematics Subject Classification. 92D25. 34A37, 34K15. Keywords. Singular fractional differential system, impulsive boundary value problem, Riemann-Liouville fractional differential equation with multiple base points, fixed point theorem.

show abstract

“…Both p and q maybe singular at t = 0, t 1 , t 2 . The impulse functions in this paper are different from those ones in known paper [18,22].…”

Section: Introductionmentioning

confidence: 66%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

New results on the existence of solutions of boundary value problems for singular fractional differential systems with impulse effects

Liu

2015

Tbilisi Math. J.

View full text Add to dashboard Cite

show abstract

“…For example, in , the authors studied the existence or uniqueness of solutions of BVPs for IFDEs with Caputo type fractional derivatives and multiple starting points. In , the authors established existence and uniqueness results for some boundary value problems of impulsive fractional differential equations involving the Caputo fractional derivatives with single starting point.…”

Section: Introductionmentioning

confidence: 99%

General methods for converting impulsive fractional differential equations to integral equations and applications

Liu

2017

Mathematische Nachrichten

View full text Add to dashboard Cite

In this paper, we propose the concepts of Caputo fractional derivatives and Caputo type Hadamard fractional derivatives for piecewise continuous functions. We obtain general solutions of four classes of impulsive fractional differential equations (Theorem 3.1-Theorem 3.4) respectively. These results are applied to converting boundary value problems for impulsive fractional differential equations to integral equations. Some comments are made on recently published papers (see Section 4). K E Y W O R D SHigher order fractional differentiai equation, impulse effect, general solution M S C ( 2 0 1 0 ) 26A33, 34A08, 34B15, 34B16, 34B37, 39B99, 45G10

show abstract

“…Bonanno et al in [16] proved existence results for impulsive fractional differential equations by a variational approach. Henderson and Ouahab in [17] proved a Filippov-type theorem for an impulsive fractional differential inclusion with initial conditions in R (see also [18][19][20]). In the survey [21] Agarwal et al collect some recent existence results for fractional differential equations and inclusions with impulses and various boundary conditions in R, applying the Banach contraction principle, the Schaefer fixed point theorem, and the Leray-Schauder alternative.…”

Section: Introductionmentioning

confidence: 99%

On Noncompact Fractional Order Differential Inclusions with Generalized Boundary Condition and Impulses in a Banach Space

Benedetti

Obukhovskiĭ

Taddei

2015

Journal of Function Spaces

View full text Add to dashboard Cite

show abstract

Existence of solution to a periodic boundary value problem for a nonlinear impulsive fractional differential equation

Cited by 19 publications

References 17 publications

New results on the existence of solutions of boundary value problems for singular fractional differential systems with impulse effects

New results on the existence of solutions of boundary value problems for singular fractional differential systems with impulse effects

General methods for converting impulsive fractional differential equations to integral equations and applications

On Noncompact Fractional Order Differential Inclusions with Generalized Boundary Condition and Impulses in a Banach Space

Contact Info

Product

Resources

About