On the existence of solutions for fractional differential inclusions with sum and integral boundary conditions

Ntouyas, Sotiris K.; Etemad, Sina

doi:10.1016/j.amc.2015.05.036

Cited by 53 publications

(38 citation statements)

References 21 publications

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“…On the other hand 16) where δ ij 's are given in (2.14)-(2.15) for i, j = 1, 2. Next, we prove that F maps bounded sets into equicontinuous sets of X.…”

Section: Resultsmentioning

confidence: 99%

“…The increasing interest of fractional differential equations and inclusions are motivated by their applications in various fields of science such as physics, chemistry, engineering, biology, economics, fluid mechanics, control theory, etc. For this reason, in the recent years, many papers have been published about fractional differential equations and inclusions by mathematicians and other researchers (for example, see [1,2,4,5,6,7,8,9,12,16,17,18,19,22] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

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Existence results for three-point boundary value problems for nonlinear fractional differential equations

Etemad¹,

Ntouyas²,

Tariboon³

2016

J. Nonlinear Sci. Appl.

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“…On the other hand 16) where δ ij 's are given in (2.14)-(2.15) for i, j = 1, 2. Next, we prove that F maps bounded sets into equicontinuous sets of X.…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Existence results for three-point boundary value problems for nonlinear fractional differential equations

Etemad¹,

Ntouyas²,

Tariboon³

2016

J. Nonlinear Sci. Appl.

Self Cite

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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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“…The interest in this topic results from the applicability of nonlocal and integral conditions in mathemati-cal modeling of many real world situations arising in applied and biological sciences. For details and examples, see [11][12][13][14][15][16][17][18][19][20][21][22][23] and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

On a nonlocal integral boundary value problem of nonlinear Langevin equation with different fractional orders

2019

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In this paper we develop the existence theory for a nonlinear Langevin equation involving Caputo fractional derivatives of different orders and Riemann-Liouville fractional integral supplemented with nonlocal multi-point and multi-strip boundary conditions. We make use of the modern methods of functional analysis to obtain the existence and uniqueness results for the given problem, which are well illustrated with the aid of examples. Our results are new and correspond to some new ones for specific choices of the parameters involved in the problem. Publisher's NoteSpringer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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On the existence of solutions for fractional differential inclusions with sum and integral boundary conditions

Cited by 53 publications

References 21 publications

Existence results for three-point boundary value problems for nonlinear fractional differential equations

Existence results for three-point boundary value problems for nonlinear fractional differential equations

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

On a nonlocal integral boundary value problem of nonlinear Langevin equation with different fractional orders

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