Monotone solutions of iterative fractional equations found by modified Darbo-type fixed-point theorems.

*(English)*Zbl 1376.34011Summary: There are many forms of solutions that occur obviously, and in various situations one cannot just switch to one of them and establish solutions in that sense. It is valuable to study solutions with strong differentiability properties, but it might be difficult to confirm their existence. Therefore, one essentially considers solutions in a weaker sense. In this note, we establish the existence of monotone solutions of the dynamic system of the bacterial growth of iterative fractional differential equations, found by a new coupled and triple fixed point theorem in the sense of Darbo processing. We propose these theorems (Darbo type) for a new contraction by using a measure of non-compactness in Banach spaces. The new outcomes show some special well-known recent results.

##### MSC:

34A08 | Fractional ordinary differential equations and fractional differential inclusions |

47H10 | Fixed-point theorems |

##### Keywords:

coupled fixed point theorem; measure of non-compactness; iterative fractional equation; fractional calculus; fractional differential operator
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\textit{H. K. Nashine} and \textit{R. W. Ibrahim}, J. Fixed Point Theory Appl. 19, No. 4, 3217--3229 (2017; Zbl 1376.34011)

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##### References:

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