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Fractional differential equations have been of great interest amongst researchers over the last two decades. Due to the widespread applications in science and technology, research within these types of equations has led to new developments in the theory of fractional difference equations as well as fractional

This issue on recent developments and applications on discrete fractional equations and related topics aims to provide better understanding for fractional differential equations, fractional difference equations, fractional

There are many different approaches to obtain fractional derivatives. T. Abdeljawad et al. gave the definitions of the delta left and nabla right fractional differences and sums with binomial coefficients. Indeed, they used the discrete version of the

The qualitative theory including the existence and uniqueness of solutions, stability, asymptotic, oscillation, and periodicity is a crucial subject in the study of differential equations. F. Chen and Y. Zhou discussed the existence of solutions for antiperiodic boundary value problem and the Ulam stability for nonlinear fractional difference equations. Z. Han et al. investigated the oscillation for a class of fractional differential equations. However, B. Wu studied a class of pseudodifferential equations involving

The fractional differential equations play an important role in various fields of science and engineering. With the help of fractional calculus, it has been found that many natural phenomena can be described using certain mathematical models. Indeed, H. A. Jalab and R. W. Ibrahim introduced a texture enhancement technique for medical images by using fractional differential masks based on Srivastava-Owa fractional operators. A 2D isotropic gradient mask based on generalized fractional operators is constructed. Texture enhancement performance was measured by applying experiments according to visual perception and by using Sobel/Canny edge filters and gray level cooccurrence matrix. They also discussed the capability of the fractional differential mask for texture enhancement. The experiments and analysis showed that the operator can extract subtle information and make the edges prominent. H. A. Jalab and R. W. Ibrahim introduced a system of fractional order derivative for a uniformly sampled polynomial signal by employing the generalized fractional differential operator and discussed the convergence of the system to a fractional time differentiator.

In conclusion, we hope that the papers published in this issue will enrich the readers’ knowledge and stimulate researchers to extend, generalize, and apply the established results.

We would like to thank the editorial board members of this journal for their support and help throughout the preparation of this special issue.