This study outlines the local fractional integro-differential equations carried out by the local fractional calculus. The analytical solutions within local fractional Volterra and Abel’s integral equations via the Yang-Laplace transform are discussed. Some illustrative examples will be discussed. The obtained results show the simplicity and efficiency of the present technique with application t...

Based on the definition of the instantaneous frequency (signal phase derivative) as a local moment of the Wigner distribution, we derive the relationship between the instantaneous frequency and the derivative of the squared modulus of the fractional Fourier transform (fractional Fourier transform power spectrum) with respect to the angle parameter. We show that the angular derivative of the fra...

In the paper, we present a new definition of fractional derivative with a smooth kernel which takes on two different representations for the temporal and spatial variable. The first works on the time variables; thus it is suitable to use the Laplace transform. The second definition is related to the spatial variables, by a non-local fractional derivative, for which it is more convenient to work...

In this paper, we establish the new forms of Riemann-type fractional integral and derivative operators. The novel operator is proved to be bounded in Lebesgue space some classical differential operators are obtained as special cases. properties like semi-group, inverse certain others discussed its weighted Laplace transform evaluated. Fractional integro-differential free-electron laser (FEL) ki...

We study different maximum principles for non-local non-linear operators with non-standard growth that arise naturally in the context of fractional Orlicz–Sobolev spaces and whose most notable representative is g-Laplacian: (−Δg)su(x)≔p.v∫Rngu(x)−u(y)|x−y|sdy|x−y|n+s,being g derivative a Young function. further derive qualitative properties solutions such as Liouville type theorem symmetry resu...

In this work we study necessary and sufficient optimality conditions for variational problems dealing with a new fractional derivative. This derivative combines two known operators: distributed-order derivatives arbitrary kernels. After proving integration by parts formula, obtain the Euler-Lagrange equation natural boundary fundamental problem. Also, integral holonomic constraints a...