Fractional order continuity of a time semi-linear fractional diffusion-wave system

Semilinear parabolic diffusion systems on the sphere with Caputo-Fabrizio operator

“…Partial diferential equations on the sphere and their analysis were investigated by many authors, such as many authors, for example [13,14,15,16,17,9,12,33,34,35,22,28]. These equations play a role in modeling a number of physical phenomena that occur in the earth's surface or in earthquakes and seismic events.…”

Local Fractional Aboodh Transform and its Applications to Solve Linear Local Fractional Differential Equations

“…The search for analytical solutions to fractional dierential equations is often dicult, so in many cases researchers focus on studying the existence, uniqueness and properties of solutions [5,12,18,21,27,28], while others tend to employ numerical methods to search for approximate solutions. Transformations dened by integrals play an important role in the resolution of ordinary dierential equations, partial dierential equations and in the resolution of integral dierential equations with integer order or fractional order.…”

Semilinear Fractional Evolution Inclusion Problem in the Frame of a Generalized Caputo Operator

“…Fractional calculus is a field of mathematical analysis that embraces the integrals and derivatives of functions of any real or complex order. For the past few decades, this field has been one of the hand-over-fist sprawling fields of mathematics by virtue of the amazing findings obtained when researchers enrolled the fractional operators in their attempts to construe some problems that arise in nature (see [1][2][3][4][5][6]). As a matter of fact, the classical fractional calculus consisted of one main integral operator, namely, the Riemann-Liouville fractional integral, and two fractional derivatives, namely, the Riemann-Liouville and Caputo derivatives.…”