On existence and uniqueness of fractional integrodifferential equations with an integral fractional boundary condition

Abstract

The aim of the present paper is to establish the existence and uniqueness of solutions of fractional integrodifferential equations with an integral fractional boundary condition in Banach spaces. KeywordsFractional integrodifferential equations, fractional integral boundary value conditions, existence of solution.

Study of fractional integro‐differential equations under Caputo‐Fabrizio derivative

“…14,15 There have been traced of very important applications of the said equations in fluid mechanics and plasma physics. 16 Currently, researchers have studied FIDEs and developed their existence and uniqueness results corresponding to ordinary derivative of fractional order including Caputo, Riemann-Liouville, and Hadamard type fractional derivative (see literature [17][18][19][20][21][22][23][24][25][26][27] ). In recent times, these forms of derivative have been prolonged to some new type containing non-singular kernels of exponential and Mittag-Lefler types.…”

On nonlinear mixed fractional integro-differential equations with positive constant coefficient

“…Recently, many researchers have studied the Cauchy problem and long time behavior for nonlinear fractional differential and integro-differential equations and obtained many interesting results by using all kinds of fixed point theorems, for example, by Aghajani et al [2], Balachandran and Park [4], Barbagallo et al. [7], Cabrera et al [8], Dong et al [11], Furati and Tatar [12], Jagtap and Kharat [14], Kharat [15], Kharat et al [16], Kendre and Kharat [19], Kendre et al [18,20,21], Liang et al [24], N'Guérékata [26,27], Pierri and O'Regan [29], Ragusa and Scapellato [31], Ren et al [32], Ruggieri et al [33], Tate et al [37], Turmetov [40], Wang and Li [41], Zhou et al [42,43], Zhou and Jiao [44] and the references therein.…”