2019
DOI: 10.1186/s13662-019-2090-8
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Existence results for a fraction hybrid differential inclusion with Caputo–Hadamard type fractional derivative

Abstract: In this manuscript, we talk over the existence of solutions of a class of hybrid Caputo-Hadamard fractional differential inclusions with Dirichlet boundary conditions. Our results are based on the Arzelá-Ascoli theorem and some suitable theorems of fixed point theory. As well, to illustrate our results, we confront the exceptional case of the fractional differential inclusions with examples.

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Cited by 69 publications
(47 citation statements)
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“…It has an old history and several fractional derivations where defined, such as the Caputo, the Riemann-Liouville and the Caputo and Fabrizio derivations. These derivations appeared recently in much work on integrodifferential equations by using different views which young researchers could use for their work [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. The fractional q-calculus has been applied to almost very field of non-linear mathematics analysis [28][29][30][31][32][33][34][35][36][37][38].…”
Section: Introductionmentioning
confidence: 99%
“…It has an old history and several fractional derivations where defined, such as the Caputo, the Riemann-Liouville and the Caputo and Fabrizio derivations. These derivations appeared recently in much work on integrodifferential equations by using different views which young researchers could use for their work [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. The fractional q-calculus has been applied to almost very field of non-linear mathematics analysis [28][29][30][31][32][33][34][35][36][37][38].…”
Section: Introductionmentioning
confidence: 99%
“…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%
“…In 1910, Jackson introduced the subject of q-difference equations [1]. Later, many researchers studied q-difference equations [2][3][4][5][6][7][8][9][10][11][12]. On the other hand, there appeared recently much work on q-differential equations by using different views and fractional derivatives; young researchers could use the main idea in their work (see, for example, [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]).…”
Section: Introductionmentioning
confidence: 99%