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 ...

This study outlines the local fractional integro-differential equations carried out by the local fractional calculus. The analytical solutions within local fractional Volterra and Abel’s integral equations via the Yang-Laplace transform are discussed. Some illustrative examples will be discussed. The obtained results show the simplicity and efficiency of the present technique with application t...

Fractional calculus has been widely used in mathematical modeling of evolutionary systems with memory effect on dynamics. The main interest this work is to attest, through a statistical approach, how the hysteresis phenomenon, which describes type present biological systems, can be treated by fractional calculus. We also analyse contribution historical values function evaluation operators accor...

We present a semilocal convergence study of Newton-type methods on a generalized Banach space setting to approximate a locally unique zero of an operator. Earlier studies require that the operator involved is Fréchet differentiable. In the present study we assume that the operator is only continuous. This way we extend the applicability of Newton-type methods to include fractional calculus and ...

An important class of fractional differential and integral operators is given by the theory calculus with respect to functions, sometimes called ?-fractional calculus. The operational approach has proved useful for understanding extending this topic study. Motivated equations, we present an Laplace transforms functions their relationship functions. This makes generalised much easier analyse app...