Generalized Fractional Operators and Special Functions: Theory, Methods, and Applications

Dear Colleagues, 

Fractional calculus has rapidly evolved as a powerful mathematical tool for describing memory and hereditary properties inherent in diverse natural and engineered systems. Its flexible operators extend classical differentiation and integration to non-integer orders, offering new avenues in modeling complex phenomena in physics, engineering, biology, economics, and applied sciences. At the same time, special functions—such as hypergeometric functions, Mittag-Leffler functions, Bessel functions, and generalized orthogonal polynomials—play a pivotal role in solving fractional differential equations and in characterizing solutions with analytical depth and computational tractability. The intersection of fractional calculus with special functions has produced groundbreaking results in the development of exact solutions, numerical schemes, stability analysis, and applications across multiple disciplines. This Special Issue aims to bring together leading researchers to present recent advances, novel methods, and applications that highlight the synergy between fractional operators and special functions. 

The scope and potential topics include (but are not limited to) the following:

New definitions and generalizations of fractional operators. Analytical and numerical solutions of fractional differential and integral equations using special functions. Inequalities, convexity, and approximation theory in the fractional framework. Applications of special functions (Mittag-Leffler, Wright, Fox H-function, etc.) in fractional modeling. Fractional models in fluid dynamics, control theory, viscoelasticity, and heat/mass transfer. Fractal and fractional approaches in physics, finance, and biological systems. Computational algorithms and stability analysis of fractional systems. Connections between fractional calculus, operator theory, and integral transforms.

Objective:

The objective of this Special Issue is to provide a comprehensive platform for disseminating theoretical advancements, methodological innovations, and real-world applications that emerge from the interplay of fractional calculus and special functions.

Dr. Adil Jhangeer
Guest Editor

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