Fractional differential equations have been discussed in this study. We utilize the Riemann–Liouville fractional calculus to implement it within the generalization of the well known class of differential equations. The Rayleigh differential equation has been generalized of fractional second order. The existence of periodic and positive outcome is established in a new method. The solution is described in a fractional periodic Sobolev space. Positivity of outcomes is considered under certain requirements. We develop and extend some recent works. An example is constructed.
In this paper, we consider a low initial population model. Our aim is to study the periodicity computation of this model by using neutral differential equations, which are recognized in various studies including biology. We generalize the neutral Rayleigh equation for the third-order by exploiting the model of fractional calculus, in particular the Riemann-Liouville differential operator. We establish the existence and uniqueness of a periodic computational outcome. The technique depends on the continuation theorem of the coincidence degree theory. Besides, an example is presented to demonstrate the finding.
In this study, we generalize a time-delay system joining n-deviating arguments by utilizing the concept of the Riemann-Liouville fractional calculus. The class of equations is taken in view of the Rayleigh-type equation. Our tool is based on the fixed-point theorems. The existence of the outcomes is delivered under some certain conditions. The application is illustrated in the sequel.
The existence of symmetric-periodic outcomes for a class of fractional differential equations has been increasingly studied. Such study has used various methods such as fixed point theory, critical point theory, and approximation theory. In this work, we study the m-pseudo almost automorphic (m-PKK) outcomes for a category of fractional neutral differential equations. To satisfy this aim, we introduce composition results under suitable conditions and employ them to establish some extant outcomes using interpolation theory mixed with fixed point technique. Examples are illustrated.
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