Existence results for hybrid fractional integro-differential equations

Abstract

In this paper we study existence results for initial value problems for hybrid fractional integro-differential equations. A couple of hybrid fixed point theorems for the sum of three operators are used for proving the main results. Examples illustrating the results are also presented. MSC: 34A08; 34A12

Recent Developments of Lyapunov–Type Inequalities for Fractional Differential Equations

“…Corollary 4. If λ is an eigenvalue of the problem (37), then Sitho et al [23] established some Lyapunov-type inequalities for the following hybrid fractional boundary value problem…”

Boundedness and power-type decay of solutions for a class of generalized fractional Langevin equations

“…[5,9,24,25,36,38,39] and the references therein. There is a large volume of literature on existence of solutions for various classes of fractional differential and integro-differential equations (see for instance [1][2][3][4]8,12,17,18,20,35,37] ). Agarwal et al surveyed in [1] many of these existence results.…”

Existence Results of Initial Value Problems for Hybrid Fractional Sum-Difference Equations

“…For some recent developments on the topic, see [52][53][54][55][56][57]. Recently, there are several research works related to boundary value problems for hybrid differential equations (see [58][59][60][61][62][63][64][65]). For example, Sun et al [60] studied the existence of solutions for the boundary value problem of fractional hybrid differential equations…”

“…Sitho et al [64] studied existence results for the following initial value problem for hybrid fractional integrodifferential equations,…”