Search
Search Results
-
Fractional Leibniz Rules in the Setting of Quasi-Banach Function Spaces
Fractional Leibniz rules are reminiscent of the product rule learned in calculus classes, offering estimates in the Lebesgue norm for fractional...
-
Fractional Leibniz-type Rules on Spaces of Homogeneous Type
Let ( M , ρ , μ ) be a space of homogeneous type satisfying the reverse doubling condition and the non-collapsing condition. In view of the lack of the...
-
On univariate fractional calculus with general bivariate analytic kernels
Several fractional integral and derivative operators have been defined recently with a bivariate structure, acting on functions of a single variable...
-
Leibniz on Number Systems
This chapter examines the pioneering work of Gottfried Wilhelm Leibniz (1646–1716) on various number systems, in particular binary, which he...
-
Fractional Calculus of the Lerch Zeta Function
This paper deals with the fractional derivative of the Lerch zeta function. We compute the fractional derivative of the Lerch zeta function using a...
-
Initial and boundary value problem of fuzzy fractional-order nonlinear Volterra integro-differential equations
The fractional derivative in Caputo sense for the class of fuzzy fractional order Volterra integro-differential equations of the first kind is...
-
Fractional Calculus
After introducing the concept of fractional integral we define the Riemann–Liouville fractional integrals, Riemann–Liouville fractional derivatives,...
-
Weighted Leibniz-type rules for bilinear flag multipliers
We establish Leibniz type rules for bilinear flag multipliers with limited regularity in the Lebesgue spaces with flag weights. As applications, we...
-
Leibniz-Type Rules for Bilinear Fourier Multiplier Operators with Besov Regularity
We establish the Leibniz-type rules for bilinear Fourier multiplier operators with Besov regularity in Lebesgue spaces and mixed Lebesgue spaces.
-
Fractional Integrals and Derivatives
In this chapter, we list various types of fractional integrals and fractional derivatives available in the literature. In fact, the purpose is to...
-
Leibniz on Number Systems
This chapter examines the pioneering work of Gottfried Wilhelm Leibniz (1646–1716) on various number systems, in particular binary, which he...
-
On the order reduction of approximations of fractional derivatives: an explanation and a cure
Finite-difference based approaches are common for approximating the Caputo fractional derivative. Often, these methods lead to a reduction of the...
-
Symmetries of Fractional Guéant–Pu Model with Gerasimov–Caputo Time-Derivative
For the time fractional Guéant–Pu option pricing model we obtain the Lie algebra of the group of equivalence transformations, which is used to obtain...
-
On the variable-order fractional derivatives with respect to another function
In this paper, we present various concepts concerning generalized fractional calculus, wherein the fractional order of operators is not constant, and...
-
Discrete Fractional Calculus
In this chapter we will develop the theory of discrete fractional calculus, using the operators introduced in the works by Miller and Ross...
-
A Pro Rata Definition of the Fractional-Order Derivative
In this paper a novel definition of the fractional-order derivative operator will be introduced. This operator will be called “pro rata” due to its...
-
A New Representation for the Solutions of Fractional Differential Equations with Variable Coefficients
A recent development in differential equations with variable coefficients by means of fractional operators has been a method for obtaining an exact...