## Integral and Fractional Integral Calculus in Theory and Application to Generalized Functions

#### Call for Papers

In recent years, the concept of integral and fractional integral operators have been extensively investigated in many engineering applications and science. For example, the fractional Fourier transform, being a generalization of the ordinary Fourier transform, was introduced 70 years ago and, in the last decade, has been actively applied in signal processing, optics, and quantum mechanics which gives a more complete representation of the signal in phase space and enlarges the number of applications of the ordinary Fourier transform. Nowadays, various fractional integral transforms such as the fractional Hartley transform, the fractional Mellin transform, the fractional Whittaker transform, and the fractional Laplace transform play important roles in signal processing, image reconstruction, pattern recognition, acoustic signal processing, and some others.

On the other hand, the field of generalized functions, as a whole new branch of modern analysis, has a longstanding tradition starting in the mid-twentieth century and is actively pursued by many research groups all over the world. The field has always developed along the requirements of applications, notably in linear and nonlinear partial differential equations, geometry (linear/nonlinear distributional geometry), mathematical physics (general relativity, geophysics, fluid dynamics, and quantum theory), and stochastic analysis (generalized stochastic processes and stochastic partial differential equations) as well as in harmonic analysis, both in theoretical and in numerical aspects .

The purpose of this special issue is to promote research in the field of the theory of integral and fractional integral operators, integral equations , and their applications to generalized functions (including distributions and Mikusinski´s approach to generalized functions ).

In this special issue we will accept good quality papers containing original research results with exceptional merit.

Potential topics include but are not limited to the following:

• Mathematical analysis of fractional integral operators, theoretical approach
• Mathematical analysis of fractional integral equations, theoretical approach
• Integral and fractional integrals associated with functions of special function type
• Application of Integral and fractional integrals to function spaces
• Integral equations of generalized functions
• Mikusinski approach to generalized functions (Boehmians), theoretical approach
• Integrals involving special functions with application to generalized functions
• Mathematical analysis of Jackson q-integral operators and application to generalized functions
• q-special functions and applications

Authors can submit their manuscripts through the Manuscript Tracking System at https://mts.hindawi.com/submit/journals/jmath/analysis/ifio/.

 Submission Deadline Friday, 13 July 2018 Publication Date November 2018

Papers are published upon acceptance, regardless of the Special Issue publication date.