scholarly journals New fractional calculus results involving Srivastava’s general class of multivariable polynomials and The H̅ - function

2015 ◽  
Vol 11 (1) ◽  
pp. 19-32
Author(s):  
V. B. L. Chaurasia ◽  
Vinod Gill
Keyword(s):  
Differential Operator ◽  
Fractional Calculus ◽  
Wide Class ◽  
Mathematical Analysis ◽  
Fractional Differential Operator ◽  
Fractional Calculus Operators ◽  
Fractional Differential ◽  
Interesting Special Case ◽  
Special Case ◽  
Interesting Account

Abstract A significantly large number of earlier works on the subjects of fractional calculus give interesting account of the theory and applications of fractional calculus operators in many different areas of mathematical analysis. In the present paper, we study and develop an important result involving a fractional differential operator for the product of general multivariable polynomials, general polynomial set and two -functions. The result discussed here can be used to investigate a wide class of new and known results, hitherto scattered in the literature. For the sake of illustration, six interesting special case have also been recorded here of our main findings.

scholarly journals On Multivalent Analytic Functions Considered by a Multi-Arbitrary Differential Operator in a Complex Domain

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 315
Author(s):  
Najla M. Alarifi ◽  
Rabha W. Ibrahim
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Integral Operators ◽  
Upper And Lower Bounds ◽  
Fractional Operator ◽  
Convolution Operators ◽  
Linear Convolution ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Special Case

(1) Background: There is an increasing amount of information in complex domains, which necessitates the development of various kinds of operators, such as differential, integral, and linear convolution operators. Few investigations of the fractional differential and integral operators of a complex variable have been undertaken. (2) Methods: In this effort, we aim to present a generalization of a class of analytic functions based on a complex fractional differential operator. This class is defined by utilizing the subordination and superordination theory. (3) Results: We illustrate different fractional inequalities of starlike and convex formulas. Moreover, we discuss the main conditions to obtain sandwich inequalities involving the fractional operator. (4) Conclusion: We indicate that the suggested class is a generalization of recent works and can be applied to discuss the upper and lower bounds of a special case of fractional differential equations.

Abstract Fractional Monotone Approximation with Applications

2021 ◽  
Vol 5 (4) ◽  
pp. 158
Author(s):  
George A. Anastassiou
Keyword(s):  
Differential Operator ◽  
Fractional Calculus ◽  
Modulus Of Continuity ◽  
Approximation Theory ◽  
Singular Kernel ◽  
Monotone Approximation ◽  
Constrained Approximation ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Left And Right

Here we extended our earlier fractional monotone approximation theory to abstract fractional monotone approximation, with applications to Prabhakar fractional calculus and non-singular kernel fractional calculi. We cover both the left and right sides of this constrained approximation. Let f∈Cp−1,1, p≥0 and let L be a linear abstract left or right fractional differential operator such that Lf≥0 over 0,1 or −1,0, respectively. We can find a sequence of polynomials Qn of degree ≤n such that LQn≥0 over 0,1 or −1,0, respectively. Additionally f is approximated quantitatively with rates uniformly by Qn with the use of first modulus of continuity of fp.

scholarly journals -Dimensional Fractional Lagrange's Inversion Theorem

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
F. A. Abd El-Salam
Keyword(s):  
Differential Operator ◽  
Fractional Calculus ◽  
Unknown Function ◽  
Taylor Expansion ◽  
Higher Dimensions ◽  
Lagrange Inversion ◽  
Inversion Theorem ◽  
Fractional Differential Operator ◽  
Independent Variable ◽  
Fractional Differential

Using Riemann-Liouville fractional differential operator, a fractional extension of the Lagrange inversion theorem and related formulas are developed. The required basic definitions, lemmas, and theorems in the fractional calculus are presented. A fractional form of Lagrange's expansion for one implicitly defined independent variable is obtained. Then, a fractional version of Lagrange's expansion in more than one unknown function is generalized. For extending the treatment in higher dimensions, some relevant vectors and tensors definitions and notations are presented. A fractional Taylor expansion of a function of -dimensional polyadics is derived. A fractional -dimensional Lagrange inversion theorem is proved.

On the kinetics of Hadamard-type fractional differential systems

2020 ◽  
Vol 23 (2) ◽  
pp. 553-570 ◽  
Author(s):  
Li Ma
Keyword(s):  
Differential Operator ◽  
Numerical Simulations ◽  
Type Inequality ◽  
The Other ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Kinetics Of ◽  
Theoretical Results

AbstractThis paper is devoted to the investigation of the kinetics of Hadamard-type fractional differential systems (HTFDSs) in two aspects. On one hand, the nonexistence of non-trivial periodic solutions for general HTFDSs, which are considered in some functional spaces, is proved and the corresponding eigenfunction of Hadamard-type fractional differential operator is also discussed. On the other hand, by the generalized Gronwall-type inequality, we estimate the bound of the Lyapunov exponents for HTFDSs. In addition, numerical simulations are addressed to verify the obtained theoretical results.

scholarly journals On a fractional-order p-Laplacian boundary value problem at resonance on the half-line with two dimensional kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
O. F. Imaga ◽  
S. A. Iyase
Keyword(s):  
Differential Operator ◽  
Boundary Value Problem ◽  
Fractional Order ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Half Line ◽  
At Resonance ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Problem At Resonance

AbstractIn this work, we consider the solvability of a fractional-order p-Laplacian boundary value problem on the half-line where the fractional differential operator is nonlinear and has a kernel dimension equal to two. Due to the nonlinearity of the fractional differential operator, the Ge and Ren extension of Mawhin’s coincidence degree theory is applied to obtain existence results for the boundary value problem at resonance. Two examples are used to validate the established results.

scholarly journals On Caputo modification of Hadamard-type fractional derivative and fractional Taylor series

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Rashida Zafar ◽  
Mujeeb ur Rehman ◽  
Moniba Shams
Keyword(s):  
Differential Operator ◽  
Fractional Derivative ◽  
Taylor Series ◽  
General Framework ◽  
Taylor Expansion ◽  
Fractional Integral ◽  
Haar Wavelet ◽  
Wavelet Method ◽  
Fractional Differential Operator ◽  
Fractional Differential

Abstract In this paper a general framework is presented on some operational properties of Caputo modification of Hadamard-type fractional differential operator along with a new algorithm proposed for approximation of Hadamard-type fractional integral using Haar wavelet method. Moreover, a generalized Taylor expansion based on Caputo–Hadamard-type fractional differential operator is also established, and an example is presented for illustration.

Sign in / Sign up

Export Citation Format

Share Document