Implicit fractional differential equations

Mathematical Methods in the Applied Sciences, 2023
This paper focuses on revisiting and improving the results regarding the existence of a solution to the implicit fractional differential equations (FDEs) given in the following form: for all with the initial condition , where is the Caputo fractional derivative (CFD).
Canan Çelik, Faruk Develi
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Implicit Caputo-Fabrizio fractional differential equations with delay

Studia Universitatis Babes-Bolyai Matematica, 2023
"This article deals with some existence and uniqueness results for several classes of implicit fractional differential equations with delay. Our results are based on some fixed-point theorems. To illustrate our results, we present some examples in the last section. Keywords: Caputo-Fabrizio fractional order derivative, implicit, delay, fixed point."
Salim Krim +3 more
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On Implicit $��$-Caputo Fractional Integro-differential Equations

2021
In this paper, we investigate the existence and uniqueness of solution of nonlinear $ $-Caputo fractional differential equation with the help of Banach fixed point theorem. Moreover, by using $ $-Gronwall inequality, we studied some qualitative properties of solutions such as estimate and stability.
Pachpatte, Deepak B., Yewale, Bhagwat R.
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Theory of Nonlinear Implicit Fractional Differential Equations

Differential Equations and Dynamical Systems, 2016
In this paper, the authors study existence, interval of existence, uniqueness and continuous dependence of solutions on initial conditions of the implicit fractional differential equation of the form \[^cD^{\alpha}x(t)= f(t,x(t),^cD^{\alpha}x(t)),\ \ \ x(0) = x_0 \in \mathbb{R}, t \in [0, T], \] where \(^cD^{\alpha} \ (0
Kucche, Kishor D., Nieto, Juan J., Venktesh, Venktesh +2 more
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fixed point
existence
fractional integral

fractional differential equations
boundary value problem
fixed point theorem

initial value problem
26a33
caputo fractional derivative