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

Abstract

In this paper, we study the existence and other properties of the solution of nonlinear mixed fractional integro-differential equations with constant coefficient. Also with the help of integral inequality of mixed type, we prove the continuous dependence of the solutions on the initial conditions.

A nonlocal Cauchy problem for nonlinear generalized fractional integro-differential equations

“…The area of fractional differential equations is now considered to be very important due to its various applications in different fields of science and technology such as control theory, rheology, signal processing, modelling, fractals, chaotic dynamics, bioengineering and biomedical and so on, for example see [6,13,17] and the references therein. Recently, many researchers studied the fractional differential and integro-differential equations and obtained many interesting existence and uniqueness results, see [3,7,12,18,20,19,21,22,23] and the references therein.…”

Properties of Some $ψ$-Hilfer fractional Integrodifferential equations

“…Recently many authors have studied the fractional integrodifferential equations using various definitions of fractional operators [7]. The authors in [1,2,3,17,18,19,20,21] have studied various properties of fractional integrodifferential equations using various fractional operators. In [5,9,14,16] various results are obtained for ψ-Hilfer fractional differential equations.…”