On Hybrid Type Nonlinear Fractional Integrodifferential Equations

Abstract

In this paper, we introduce and investigate a hybrid type of nonlinear Riemann Liouville fractional integro-differential equations. We develop and extend previous work on such non-fractional equations, using operator theoretical techniques, and find the approximate solutions. We prove the existence as well as the uniqueness of the corresponding approximate solutions by using hybrid fixed point theorems and provide upper and lower bounds to these solutions. Furthermore, some examples are provided, in which the general claims in the main theorems are demonstrated.

Presence and diversity of positive solutions for a Caputo-type fractional order nonlinear differential equation with an advanced argument

“…During the last few decades diversity of positive solutions of different BVPs for fractional order nonlinear differential equation (FONLDE for short) has extensively considered by using various techniques, for instance see the articles of Agarwal et al [2,3], Afshari et al [1], Asaduzzaman and Ali [5], Bai [8], Chen et al [12], Cu et al [13], Devi et al [17], Sun et al [34], and Torres [36] as well as for lower and upper solutions to the integro-differential and iterative hybrid type fractional differential equations see, Damag et al [14] and Damag et al [15] and for positive solutions of nonlinear dissipative type equations, see Asaduzzaman et al [6].…”