On a Caputo fractional differential inclusion with integral boundary condition for convex-compact and nonconvex-compact valued multifunctions

Abstract

Abstract. In this paper, we investigate a Caputo fractional differential inclusion with integral boundary condition under different conditions. First, we investigate it for L 1 -Caratheodory convex-compact valued multifunction. Then, we investigate it for nonconvex-compact valued multifunction via some conditions. Also we give two examples to illustrate our results.

New approach to solutions of a class of singular fractional q-differential problem via quantum calculus

“…, where the multifunction F maps [0, 1] × R 3 to 2 R and is compact valued and c D α is the Caputo differential operator [54].…”

Existence results for a fraction hybrid differential inclusion with Caputo–Hadamard type fractional derivative

“…During the last decade, the subject of fractional differential equations and inclusions has been developed intensively (for example, see [1][2][3][4][5][6][7][8] and the references therein). An excellent account on the study of fractional differential equations can be found in [9][10][11][12].…”

Existence of solutions for equations and inclusions of multiterm fractional q-integro-differential with nonseparated and initial boundary conditions

“…There has been an intensive development in fractional differential equations and inclusion (for example, see [5][6][7][8][9][10][11]). During the last two decades, the fractional differential equations and inclusions, both differential and q-differential, were developed intensively by many authors for a variety of subjects (for instance, consider [12][13][14][15][16][17][18][19][20]). In recent years, there are many published papers about differential and integro-differential equations and inclusions which are valuable tools in the modeling of many phenomena in various fields of science (for more details, see [21][22][23][24][25][26][27][28][29][30][31][32] and references therein).…”

“…Over the past three years, Baleanu, Rezapour and many others, by using the Caputo-Fabrizio derivative, achieved innovative and remarkable results for solutions of fractional differential equations [22,23,25,28,30,32]. In the following year, Rezapour and Hedayati investigated the existence of solutions for the inclusion (1), where multifunction F maps [0, 1] × R 3 to 2 R and is compact-valued, while c D α is the Caputo differential operator [16]. In 2019, Samei et al discussed the fractional hybrid q-…”