Solutions to fractional Sobolev-type integro-differential equations in Banach spaces with operator pairs and impulsive conditions

Nonlinear boundary value problems for mixed-type fractional equations and Ulam-Hyers stability

“…The fractional differential equations can model some engineering and scientific disciplines in the fields of physics, chemistry, electrodynamics of complex medium, polymer rheology, etc. In particular, the forward and backward fractional derivatives provide an excellent tool for the description of some physical phenomena such as the fractional oscillator equations and the fractional Euler-Lagrange equations [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Recently, a linear boundary value problem (BVP) involving both the right Caputo and the left Riemann-Liouville fractional derivatives has been studied by some authors [10][11][12][13][14].…”