Integro-differential operators with non-singular kernels have been much discussed among fractional calculus researchers. We present a mathematical study to clearly establish the rigorous foundations of this topic. By considering function spaces and mapping results, we show that can be defined on larger than singular kernels, as differentiability conditions removed. also discover an analogue Son...

The aim of this paper is to present a new numerical method for solving the Bagley-Torvik equation. This equation has an important role in fractional calculus. The fractional derivatives are described based on the Caputo sense. Some properties of the sinc functions required for our subsequent development are given and are utilized to reduce the computation of solution of the Bagley-Torvik equati...

This paper deals with the design fractional solution of Bessel equation. We obtain explicit solutions of the equation with the help of fractional calculus techniques. Using the N-fractional calculus operator N(ν) method, we derive the fractional solutions of the equation.

Several extensions of the classical Mittag-Leffler function, including multi-parameter and multivariate versions, have been used to define fractional integral derivative operators. In this paper, we consider a function one variable with five parameters, special case Fox–Wright function. It turns out that most natural way based on requires considering it as two variables. This gives rise model b...

Fractional calculus is the generalization of integer-order calculus to rational order. This subject has at least three hundred years of history. However, it was traditionally regarded as a pure mathematical field and lacked real world applications for a very long time. In recent decades, fractional calculus has re-attracted the attention of scientists and engineers. For example, many researcher...

A spatial logic consists of four groups of operators: standard propositional connectives; spatial operators; a temporal modality; calculus-specific operators. The calculus-specific operators talk about the capabilities of the processes of the calculus, that is, the process constructors through which a process can interact with its environment. We prove some minimality results for spatial logics...