Variable-order fractional operators were conceived and mathematically formalized only in
recent years. The possibility of formulating evolutionary governing equations has led to the …

We have demonstrated that both fractional extensions of the standard rotation group SO (N)
based on the Riemann and the Caputo fractional derivative definition respectively may …

This book contains mathematical preliminaries in which basic definitions of fractional
derivatives and spaces are presented. The central part of the book contains various …

The books Fractional Calculus with Applications in Mechanics: Vibrations and Diffusion
Processes and Fractional Calculus with Applications in Mechanics: Wave Propagation …

This invaluable book provides a broad introduction to the fascinating and beautiful subject of
Fractional Calculus of Variations (FCV). In 1996, FVC evolved in order to better describe non …

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We present a new numerical tool to solve partial differential equations involving Caputo
derivatives of fractional variable order. Three Caputo-type fractional operators are …

In this work, we consider a class of nonlinear integro-differential equations of variable-order.
Existence, uniqueness and stability results are discussed. For solving the considered …

The current study discusses a novel approach for numerically solving MTVO-TFDWEs under
various conditions, such as IBCs and DBCs. It uses a class of GSJPs that satisfy the given …

This paper presents a new way to solve numerically multiterm variable-order fractional
differential equations (MTVOFDEs) with initial conditions by using a class of modified shifted …