Existence of local solutions of quasilinear integrodifferential equations in banach spaces

Regularity of Solutions of Quasilinear Delay Integrodifferential Equations

“…The nonlocal conditions were motivated by physical problems and their importance is discussed in [7,8,9]. Balachandran et al [3,4,5,6,12] studied the nonlocal Cauchy problem for various type of quasilinear integrodifferential equations. Consider the nonlocal condition of the form u(0) + g(u) = u 0 , t ∈ [0, T ] = I (11) for the quasilinear integrodifferential equation (1).…”

“…in a pair of Banach spaces (Y, X) such that Y is continuously imbedded in X. Oka [18] proved the existence of classical solution of abstract quasilinear integrodifferential equations. Balachandran and Uchiyama [5] discussed the existence and uniqueness of local mild and classical solutions of quasilinear integrodifferential equations. Recently Balachandran and Park [3] studied the existence of solutions of quasilinear integrodifferential evolution equations by using the Schauder fixed point theorem.…”

On the existence and stability of solution of boundary value problem for fractional integro-differential equations with complex order

“…An excellent description in the study of FDEs can be found in [13,23,24,28]. It is considerable that there are many works about fractional integro-differential equations (FIDEs) (see, for example, [4,25,30,38]).…”

“…Motivated by the works mentioned in [4,21,27,33,34], in this paper, we estabilish four types of Ulam stability, namely Ulam-Hyers(U-H) stability, generalized U-H stability, U-H-Rassias and generalized U-H-Rassias stability for the following BVPs for FIDEs with complex order…”