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- Title
A NEW STUDY OF A CLASS OF MULTI-FRACTIONAL DIFFERENTIAL EQUATIONS.
- Authors
HARIKRISHNAN, S.; IBRAHIM, RABHA W.; KANAGARAJAN, K.
- Abstract
In this effort, we bring up a set of conditions to study the existence and uniqueness of solutions for a class of nonlocal initial value problems regarding pantograph equation with a generalized fractional derivative. The generalized derivative is taken for two fractional powers. This class of fractional differential operators extended the standard fractional calculus. Our tool is based on the Krasnoselskii's fixed point theorem (KFPT). An example is given in the sequel. Moreover, we discuss the stability of the fractional differential equation (FDE) in view of the fractional Ulam concept of stability (FUS). We suggest the power series formula depending on the initial condition of the FDE.
- Subjects
FRACTIONAL differential equations; EXISTENCE theorems; UNIQUENESS (Mathematics); FRACTIONAL calculus; FIXED point theory
- Publication
Journal of Fractional Calculus & Applications, 2019, Vol 10, Issue 1, p135
- ISSN
2090-584X
- Publication type
Article