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The object of the preset paper is to establish a result of Double Dirichlet average of Robotnov And Hartley’s function by using fractional derivative.

In present paper, we have derived the fractional q-derivative of special functions. To begin with the theorem on term by term q-fractional differentiation has been derived. The result is an extension of an earlier result due to Yadav and Purohit [8] and Sharma and Jain [9]. As a special case, of fractional q-differentiation of Robotnov and Hartley’s function has been obtained.

This venture containing dynamic control plan for robotized driving of vision-based self-ruling vehicles, with an extraordinary concentrate on the planned controlling and braking control in crisis hindrance shirking. A self-governing vehicle is a complex multi input and multi yield (MIMO) framework, which has the elements of parameter vulnerabilities and solid non linear, and the coupled marvels of longitudinal and horizontal progression are clear in a joined cornering and braking move. A viable facilitated control framework for mechanized driving is proposed to manage these coupled and nonlinear elements and reject the unsettling influences. Initial, a dream calculation is developed to recognize the reference way and give the nearby area data amongst vehicles and reference way continuously. At that point, a novel composed controlling and braking control methodology is proposed in view of the nonlinear back venturing control hypothesis and the versatile fluffy sliding-mode control strategy, and the asymptotic merging of the proposed facilitated control framework is demonstrated by the hypothesis. At long last, test show that the proposed control methodology has great following execution and improves the riding solace and solidness of self sufficient vehicles.