A Class of Fractional Degenerate Evolution Equations with Delay

Abstract

We establish a class of degenerate fractional differential equations involving delay arguments in Banach spaces. The system endowed by a given background and the generalized Showalter–Sidorov conditions which are natural for degenerate type equations. We prove the results of local unique solvability by using, mainly, the method of contraction mappings. The obtained theory via its abstract results is applied to the research of initial-boundary value problems for both Scott–Blair and modified Sobolev systems of equations with delays.

On Strongly Continuous Resolving Families of Operators for Fractional Distributed Order Equations

“…Sufficient and necessary conditions of an unbounded closed densely defined operator A for the existence of an analytic resolving family of operators for Equation (2) are found in [17][18][19]. Thus, an extension of the theorem on generators of analytic semigroups of operators to the case of distributed order equations is obtained.…”

Analysis of Hilfer Fractional Integro-Differential Equations with Almost Sectorial Operators

“…For brevity, we take Over the last decades, mathematical modeling has been supported by the field of fractional calculus, with several successful results and fractional operators shown to be an excellent tool to describe the hereditary properties of various materials and processes. Recently, this combination has gained a large amount of importance, mainly because fractional differential equations have become powerful tools for the modeling of several complex phenomena in numerous seemingly diverse and widespread fields of science and engineering; see, for instance, the basic text books in [1][2][3][4] and recent research works in [5][6][7]. In fact, abrupt changes, such as shocks, harvesting, or natural disasters, may occur in the dynamics of evolving processes.…”

Analysis of Hilfer fractional integro-differential equations with almost sectorial operators

“…During the last decades, mathematical modeling has been supported by the field of fractional calculus, with several successful results and fractional operators showing to be an excellent tool to describe the hereditary properties of various materials and processes. Recently, this combination has gained a lot of importance, mainly because fractional differential equations have become powerful tools in modeling several complex phenomena in numerous seemingly diverse and widespread fields of science and engineering, see, for instance, the basic text books [1][2][3][4] and recent researches [5][6][7]. In fact, abrupt changes, such as shocks, harvesting, or natural disasters, may happen in the dynamics of evolving processes.…”