Decay integral solutions for a class of impulsive fractional differential equations in Banach spaces

Ke, Tran Dinh; Lân, Đỗ

doi:10.2478/s13540-014-0157-5

Cited by 32 publications

(9 citation statements)

References 24 publications

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“…On the other hand, impulsive effects widely exist in many realistic systems such as signal processing systems, automatic control systems, flying abject motions, multiagent systems, time delays and telecommunications, impulsive effects common phenomena characterized by abrupt changes at certain moments due to instantaneous perturbations. For the general aspects of impulsive differential equations, see Benchohra et al Due to the great development in the theory of fractional calculus and impulsive differential equations as well as having wide applications in several fields, recently, some researchers have studied the existence and multiplicity of solutions for FDEs with impulses by using the variational methods and fixed‐point theorems, for instance, see literature …”

Section: Introductionmentioning

confidence: 99%

Nontrivial solutions for impulsive fractional differential systems through variational methods

Heidarkhani

Salari

2020

Math Methods in App Sciences

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Fractional differential equations (FDEs) as a generalization of ordinary differential equations and integration to arbitrary noninteger orders have gained importance due to their numerous applications in many fields of science and engineering. Indeed, there are a large number of phenomena, including fluid flow, diffusive transport akin to diffusion, rheology, probability, and electrical networks, that are modeled by different equations involving fractional order derivatives. This paper deals with multiplicity results of solutions for a class of impulsive fractional differential systems. The approach is based on variational methods and critical point theory. Indeed, we establish existence results for our system under some algebraic conditions on the nonlinear part with the classical Ambrosetti–Rabinowitz (AR) condition on the nonlinear and the impulsive terms. Moreover by combining two algebraic conditions on the nonlinear term, which guarantee the existence of two weak solutions, applying the mountain pass theorem, we establish the existence of third weak solution for our system.

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Section: Introductionmentioning

confidence: 99%

Nontrivial solutions for impulsive fractional differential systems through variational methods

Heidarkhani

Salari

2020

Math Methods in App Sciences

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“…They are impulsive actions, starting abruptly at a fixed point and continuing on a finite time interval. Differential equations with instantaneous impulses have been treated in several works, see, e.g., the monographs [15][16][17], papers [18][19][20][21][22][23][24], and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Mixed-order impulsive ordinary and fractional differential equations with initial conditions

et al. 2019

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“…For the recent developments in theory and applications of impulsive FDEs, we refer the reader to the papers [22,23] and the references therein. Impulsive problems for fractional equations have been treated by topological methods in [24,25,26,27]. In [21,28], based on variational methods and critical point theory the authors studied the existence and multiplicity of solutions for the problem (D λ ), in the case h(x) = 0 for all x ∈ R.…”

Section: Introductionmentioning

confidence: 99%

Energy estimate for impulsive fractional advection dispersion equations in anomalous diffusions

2018

J. Nonlinear Funct. Anal.

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This paper deals with the existence and energy estimates of solutions for a class of impulsive fractional advection dispersion equations in anomalous diffusions, while the nonlinear part of the problem admits some hypotheses on the behavior at origin or perturbation property. In particular, for a precise localization of the parameter, the existence of a non-zero solution is established requiring the sublinearity of nonlinear part at origin and infinity. We also consider the existence of solutions for our problem under algebraic conditions with the classical Ambrosetti-Rabinowitz. By combining two algebraic conditions on the nonlinear term which guarantees the existence of two solutions as well as applying the mountain pass theorem given by Pucci and Serrin, we establish the existence of the third solution for our problem. Moreover, concrete examples of applications are also provided.

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Decay integral solutions for a class of impulsive fractional differential equations in Banach spaces

Cited by 32 publications

References 24 publications

Nontrivial solutions for impulsive fractional differential systems through variational methods

Nontrivial solutions for impulsive fractional differential systems through variational methods

Mixed-order impulsive ordinary and fractional differential equations with initial conditions

Energy estimate for impulsive fractional advection dispersion equations in anomalous diffusions

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