On a Time-Fractional Integrodifferential Equation via Three-Point Boundary Value Conditions

Băleanu, Dumitru; Rezapour, Shahram; Etemad, Sina; Alsaedi, Ahmed

doi:10.1155/2015/785738

Cited by 26 publications

(17 citation statements)

References 17 publications

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“…We know that many researchers are working on fractional differential equarions from different point of view (see, for example, ( [1][2][3][4][5][6][7][8][9][10][11][12] and [13]). In 2015, a new fractional derivative introduced entitled Caputo-Fabrizio and some researchers tried to obtain new techniques for studying of distinct integro-differential equations via the new derivation (see, for example, [14][15][16][17][18][19]) and new fractional models and optimal controls of different phenomena with the non-singular derivative operator (see, for example, [20][21][22][23][24] and [25]).…”

Section: Preliminariesmentioning

confidence: 99%

On the existence of solutions for a pointwise defined multi-singular integro-differential equation with integral boundary condition

et al. 2020

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It is important that we increase our ability for studying of complicate fractional integro-differential equation. In this paper, we investigates the existence of solutions for a pointwise defined multi-singular fractional differential equation under some integral boundary conditions. We provide an example to illustrate our main result. MSC: Primary 34A08; secondary 34A60Keywords: Multi-singularity; Pointwise defined fractional equation; The Caputo derivation 1 0 x(t) dt = m and x (0) = x (3) (0) = · · · = x (n-1) (0) = 0, where 0 < t < 1, m is a real number, n ≥ 2, α ∈ (n -1, n), 0 < β < 1, D α and

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Section: Preliminariesmentioning

confidence: 99%

On the existence of solutions for a pointwise defined multi-singular integro-differential equation with integral boundary condition

et al. 2020

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“…Nonlocal problems concerning the conditions of the behavior of different classes of solutions play an important role in the qualitative theory of ordinary differential equations [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. For more precision, we refer the readers to some specific problems such as boundedness, periodicity, almost periodicity, stability in the sense of Poisson and Ulam and to the problem of the existence of limit regimes of different types, convergence, dissipativity, and so on [17][18][19][20][21][22][23][24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Uniform persistence and almost periodic solutions of a nonautonomous patch occupancy model

et al. 2020

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In this paper, a nonlinear nonautonomous model in a rocky intertidal community is studied. The model is composed of two species in a rocky intertidal community and describes a patch occupancy with global dispersal of propagules and occupy each other by individual organisms. Firstly, we study the uniform persistence of the model via differential inequality techniques. Furthermore, a sharp threshold of global asymptotic stability and the existence of a unique almost periodic solution are derived. To prove the main results, we construct an appropriate Lyapunov function whose conditions are easily verified. The assumptions of the model are reasonable, and the results complement previously known ones. An example with specific values of parameters is included for demonstration of theoretical outcomes.

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“…and a variety of boundary conditions. For some recent works on the topic, for instance, see [1][2][3][4][5][6][7][8] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Existence Theory for a Fractional q-Integro-Difference Equation with q-Integral Boundary Conditions of Different Orders

2019

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In this paper, we study the existence of solutions for a new class of fractional q-integro-difference equations involving Riemann-Liouville q-derivatives and a q-integral of different orders, supplemented with boundary conditions containing q-integrals of different orders. The first existence result is obtained by means of Krasnoselskii's fixed point theorem, while the second one relies on a Leray-Schauder nonlinear alternative. The uniqueness result is derived via the Banach contraction mapping principle. Finally, illustrative examples are presented to show the validity of the obtained results. The paper concludes with some interesting observations. Keywords: q-integro-difference equation; boundary value problem; existence; fixed pointwhere f ∈ C([0, 1] × R, R), c D α q is the fractional q-derivative of the Caputo type, and α i , β i , γ i , η i ∈ R, i = 1, 2.

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On a Time-Fractional Integrodifferential Equation via Three-Point Boundary Value Conditions

Cited by 26 publications

References 17 publications

On the existence of solutions for a pointwise defined multi-singular integro-differential equation with integral boundary condition

On the existence of solutions for a pointwise defined multi-singular integro-differential equation with integral boundary condition

Uniform persistence and almost periodic solutions of a nonautonomous patch occupancy model

Existence Theory for a Fractional q-Integro-Difference Equation with q-Integral Boundary Conditions of Different Orders

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