We define a class of discrete operators that, in particular, include the delta and nabla fractional operators. Moreover, we prove fundamental theorem calculus for these

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...

In this paper, a new theory of generalized micropolar thermoelasticity is derived by using fractional calculus. The generalized heat conduction equation in micropolar thermoelasticity has been modified with two distinct temperatures, conductive temperature and thermodynamic temperature by fractional calculus which depends upon the idea of the RiemannLiouville fractional integral operators. A un...

The prime aim of the present paper is to continue developing theory tempered fractional integrals and derivatives a function with respect another function. This combines calculus $\Psi$-fractional calculus, both which have found applications in topics including continuous time random walks. After studying basic $\Psi$-tempered operators, we prove mean value theorems Taylor's for Riemann--Liouvi...

This Special Issue of the MDPI journal, Fractal and Fractional, on subject area “Operators Fractional Calculus Their Multidisciplinary Applications” consists 19 peer-reviewed papers, including some invited feature articles, originating from all over world [...]

In the present era, fractional calculus plays an important role in various fields. Fractional Calculus is a field of mathematic study that grows out of the traditional definitions of the calculus integral and derivative operators in much the same way fractional exponents is an outgrowth of exponents with integer value. Based on the wide applications in engineering and sciences such as physics, ...

We conduct a formal study of particular class fractional operators, namely weighted calculus, and its extension to the more general known as calculus with respect functions. emphasise importance conjugation relationships classical Riemann–Liouville use them prove many fundamental properties these operators. As examples, we consider special cases such tempered, Hadamard-type, Erdélyi–Kober also ...