In this paper, we deal with a class of nonlinear fractional nonautonomous evolution equations with delay by using Hilfer fractional derivative, which generalizes the famous Riemann-Liouville fractional derivative. The definition of mild solutions for the studied problem was given based on an operator family generated by the operator pair [Formula: see text] and probability density function. Com...

Arbitrary-order integral operators find variety of implementations in different science disciplines as well engineering fields. The study presented part this research paper derives motivation from the fact that applications fractional and special functions demonstrate a huge potential understanding many physical phenomena. Study investigation operator containing an incomplete H? (IHFs) kernel i...

We investigate the existence and nonexistence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with coupled integral boundary conditions which contain some positive constants.

and Applied Analysis 3 is called the Riemann-Liouville fractional integral of h of order α > 0 when the right side exists. Here Γ is the usual Gamma function

The focus of this research is to use a new extended beta function and develop the extensions Gauss hypergeometric functions confluent formulas that are presumed be new. Four theorems have also been defined under generalized fractional integral operators provide an image formula for extension functions. Moreover, discussed analogous statements in terms Weyl, Riemann–Liouville, Erdélyi–Kober, Sai...

By using the properties of modified Riemann-Liouville fractional derivative, some new delay integral inequalities have been studied. First, we offered explicit bounds for the unknown functions, then we applied the results to the research concerning the boundness, uniqueness and continuous dependence on the initial for solutions to certain fractional differential equations.

Abstract. Based on the fractional q–integral with the parametric lower limit of integration, we define fractional q–derivative of Riemann–Liouville and Caputo type. The properties are studied separately as well as relations between them. Also, we discuss properties of compositions of these operators. Mathematics Subject Classification: 33D60, 26A33 .

In this paper, we study the oscillation of nonlinear fractional nabla difference equations of the form [Formula: see text]where c and α are constants, [Formula: see text] is the Riemann-Liouville fractional nabla difference operator of order [Formula: see text] is a real number, and [Formula: see text]. Some sufficient conditions for oscillation are established.