A special function is a that typically entitled after an early scientist who studied its features and has specific application in mathematical physics or another area of mathematics. There are few significant examples, including the hypergeometric unique species. These types functions generalized by fractional calculus, fractal, q-calculus, (q,p)-calculus k-calculus. By engaging notion q-fracti...

In this survey talk we aim to clarify the close relationships between the operators of the generalized fractional calculus (GFC), some classes of generalized hypergeo-metric functions and generalizations of the classical integral transforms. The GFC developed in [1] is based on the essential use of the Special Functions (SF). The generalized (multiple) fractional integrals and derivatives are d...

Since Al-Salam [1] and Agarwal [2] introduced the fractional q-difference calculus, the theory of fractional q-difference calculus itself and nonlinear fractional q-difference equation boundary value problems have been extensively investigated by many researchers. For some recent developments on fractional q-difference calculus and boundary value problems of fractional q-difference equations, s...

the complex-step derivative approximation is applied to compute numerical derivatives. in this study, we propose a new formula of fractional complex-step method utilizing jumarie definition. based on this method, we illustrated an approximate analytic solution for the fractional cauchy-euler equations. application in image denoising is imposed by introducing a new fractional mask depending on s...

Many different types of fractional calculus have been proposed, which can be organised into some general classes operators. For a unified mathematical theory, results should proved in the most possible setting. Two important fractional-calculus operators are integrals and derivatives with respect to functions (dating back 1970s) those analytic kernels (introduced 2019). To cover both these sett...