• Kunde Sarita Subhashrao
• Dr. PRABHA SUDHIR RASTOGI

ABSTRACT In this study we discuss the standard approaches to the problem of fractional derivatives and fractional integrals (called simply differential integrals), namely the Riemann–Liouville, Caputo and sequential approaches. We prove basic properties of different integrals including the rules of their structure and the conditions for the equivalence of different definitions. In addition, we give a brief survey of basic methods for solving linear fractional differential equations and mention the limits of their usefulness. In particular, we formulate a theorem describing the structure of the initial-value problem for linear two-term equations. Finally, we consider some physical applications, in particular the fractional convective dispersion equation and the viscoelasticity problem. Dealing with the first issue we obtain the fundamental solution in the form of the Lévy α-stable distribution density and then we discuss the relationship between the generalized central limit theorem and the choice of the corresponding fractional model. In the section concerning viscoelasticity we mention some specific models that generalize the norm through the replacement of the classical terms by partial terms. In particular, we obtain the phase response functions of those generalized systems.

fractional differential, fractional partial, differential equations

"STUDY OF FRACTIONAL DIFFERENTIAL AND FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.9, Issue 1, page no.f717-f725, January-2022, Available :http://www.jetir.org/papers/JETIR2201600.pdf

"STUDY OF FRACTIONAL DIFFERENTIAL AND FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.9, Issue 1, page no. ppf717-f725, January-2022, Available at : http://www.jetir.org/papers/JETIR2201600.pdf