On new existence results for fractional integro-differential equations with impulsive and integral conditions

Anguraj, A.; Karthikeyan, P.; Rivero, Margarita; Trujillo, Juan J.

doi:10.1016/j.camwa.2013.01.034

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Introduction3

Theorem  Let X and Y Be Two Solutions To The Fractional H1

Lemma 26 a Piecewise Continuous Differential Functions Y :1

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Cited by 44 publications

(24 citation statements)

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“…11371027, 11471015, and 11601003). 1 School of Mathematical Sciences, Anhui University, Hefei, Anhui 230039, China.…”

Section: Theorem  Let X and Y Be Two Solutions To The Fractional Hmentioning

confidence: 99%

Existence results for hybrid fractional neutral differential equations

et al. 2017

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“…11371027, 11471015, and 11601003). 1 School of Mathematical Sciences, Anhui University, Hefei, Anhui 230039, China.…”

Section: Theorem  Let X and Y Be Two Solutions To The Fractional Hmentioning

confidence: 99%

Existence results for hybrid fractional neutral differential equations

et al. 2017

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“…The proof is similar to the proof of previous Lemma 2. 5. Assume that notations be given as in the proof of Lemma 2.5.…”

Section: Lemma 26 a Piecewise Continuous Differential Functions Y :mentioning

confidence: 99%

“…For fundamental certainties regarding to fractional systems, one can make reference to the papers [2,5,6,13,17,22,27,32], the monographs [24,30,33] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Existence results for multi-term time-fractional impulsive differential equations with fractional order boundary conditions

Singh¹,

Pandey²

2017

Malaya J. Mat.

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In this paper, we discuss the existence and uniqueness of solutions for a class of multi-term time-fractional impulsive integro-differential equations with state dependent delay subject to some fractional order integral boundary conditions. In our consideration, we apply the Banach, and Sadovskii fixed point theorems to obtain our main results under some appropriate assumptions. An example is given at the end to illustrate the applications of the established results. KeywordsFractional order differential equations, multi-term time fractional derivative, fractional impulsive conditions, fractional order integral boundary conditions.

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“…Recently, many scholars used techniques of nonlinear analysis (fixed-point theorems, Leray-Schauder theory, Adomian decomposition method, etc.) to deal with the existence of positive solutions of nonlinear boundary value problems of fractional differential equation, see [5][6][7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%