Extended Riemann-Liouville type fractional derivative operator with applications
نویسندگان
چکیده
منابع مشابه
Fractional Ince equation with a Riemann-Liouville fractional derivative
We extend the classical treatment of the Ince equation to include the effect of a fractional derivative term of order a > 0 and amplitude c. A Fourier expansion is used to determine the eigenvalue curves að Þ in function of the parameter , the stability domains, and the periodic stable solutions of the fractional Ince equation. Two important observations are the detachment of the eigenvalue cur...
متن کاملSpace-Time Fractional Reaction-Diffusion Equations Associated with a Generalized Riemann-Liouville Fractional Derivative
This paper deals with the investigation of the computational solutions of a unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the generalized Riemann–Liouville fractional derivative defined by others and the space derivative of second order by the Riesz–Feller fractional derivative and adding...
متن کاملRegularity of Mild Solutions to Fractional Cauchy Problems with Riemann-liouville Fractional Derivative
As an extension of the fact that a sectorial operator can determine an analytic semigroup, we first show that a sectorial operator can determine a real analytic α-order fractional resolvent which is defined in terms of MittagLeffler function and the curve integral. Then we give some properties of real analytic α-order fractional resolvent. Finally, based on these properties, we discuss the regu...
متن کاملRiemann-Liouville integrals of fractional order and extended KP hierarchy
An attempt is given to formulate the extensions of the KP hierarchy by introducing fractional order pseudo-differential operators. In the case of the extension with the half-order pseudo-differential operators, a system analogous to the supersymmetric extensions of the KP hierarchy is obtained. Unlike the supersymmetric extensions, no Grassmannian variable appears in the hierarchy considered he...
متن کاملSome New Delay Integral Inequalities Based on Modified Riemann-Liouville Fractional Derivative and Their Applications
By using the properties of modified Riemann-Liouville fractional derivative, some new delay integral inequalities have been studied. First, we offered explicit bounds for the unknown functions, then we applied the results to the research concerning the boundness, uniqueness and continuous dependence on the initial for solutions to certain fractional differential equations.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Open Mathematics
سال: 2017
ISSN: 2391-5455
DOI: 10.1515/math-2017-0137