Certain Recurrence Relations of Two Parametric Mittag-Leffler Function and Their Application in Fractional Calculus

Sachan, Dheerandra Shanker; Jaloree, Shailesh; Choi, Junesang

doi:10.3390/fractalfract5040215

Cited by 4 publications

(3 citation statements)

References 38 publications

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“…A detailed description about the basic properties of Mittag-Leffler function has been described in the third volume of Batemann Manuscript Project which was written by Erdélyi et al in 1955. For current research of Mittag-Leffler function, see [29].…”

Section: Introductionmentioning

confidence: 99%

Certain Integrals of Product of Mittag-Leffler Function, M-Series and I-Function of Two Variables

Sachan,

Singh

2023

jnanabha

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The object of this paper is to establish certain united integrals associated with I-function of two variables. First, we have evaluated integrals whose integrand is the product of generalized Mittag-Leer function, generalized M-series and I-function of two variables. Moreover, the integrand of the last integral is the product of generalized Mittag-Leer function, generalized M-series, H-function of one variables and I-function of two variables. We have evaluated this integral by means of Mellin transform of H-function of one variables. In consequence of general nature of I-function of two variables, some special cases also have been considered.

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Section: Introductionmentioning

confidence: 99%

Certain Integrals of Product of Mittag-Leffler Function, M-Series and I-Function of Two Variables

Sachan,

Singh

2023

jnanabha

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“…Leibniz and L'Hospital started the FC as a result of a correspondence that lasted for several months in 1695. Leibniz addressed a letter to L'Hospital in that year, posing the following query [1].…”

Section: Introductionmentioning

confidence: 99%

The Fractional Series Solutions for the Conformable Time‐Fractional Swift‐Hohenberg Equation through the Conformable Shehu Daftardar‐Jafari Approach with Comparative Analysis

Liaqat

Okyere

2022

Journal of Mathematics

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The major objective of this study is to derive fractional series solutions of the time-fractional Swift-Hohenberg equations (TFSHEs) in the sense of conformable derivative using the conformable Shehu transform (CST) and the Daftardar-Jafari approach (DJA). We call it the conformable Shehu Daftardar-Jafari approach (CSDJA). One of the universal equations used in the description of pattern formation in spatially extended dissipative systems is the Swift-Hohenberg equation. To assess the effectiveness and consistency of the suggested approach, the numerical results are compared with those obtained by the Elzaki decomposition method (EDM) in the sense of relative and absolute error functions, proving that the CSDJA is an effective substitute for techniques that use He's or Adomian polynomials to solve TFSHEs. The transition from the imprecise solution to the precise solution at various values of fractional-order derivatives is shown using the recurrence error function. Furthermore, the exact and approximative solutions are compared using 2D and 3D graphics and also numerically in the form of relative and absolute error functions. The results show that the procedure is quick, precise, and easy to implement, and it yields outstanding results. The recommended approach's strength, which gives it an advantage over the Adomian decomposition and homotopy perturbation methods, is its algorithm for dealing with nonlinear problems without the use of Adomian polynomials or He's polynomials. The advantage of this method is that it does not make any assumptions about physical parameters. As a result, it can be used to solve both weakly and strongly nonlinear problems and circumvent some of the drawbacks of perturbation techniques.

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“…The Mittag-Leffler function appears in the solutions of fractional differential equations, the same as how likely the exponential function appears in solving differential equations. Fractional integral operators containing Mittag-Leffler function are also developed and applied to study well-known real world problems, see [14][15][16][17][18][19] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Fejér–Hadamard Type Inequalities for (α, h-m)-p-Convex Functions via Extended Generalized Fractional Integrals

Farid

Yussouf²,

Nonlaopon

2021

Fractal Fract

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Integral operators of a fractional order containing the Mittag-Leffler function are important generalizations of classical Riemann–Liouville integrals. The inequalities that are extensively studied for fractional integral operators are the Hadamard type inequalities. The aim of this paper is to find new versions of the Fejér–Hadamard (weighted version of the Hadamard inequality) type inequalities for (α, h-m)-p-convex functions via extended generalized fractional integrals containing Mittag-Leffler functions. These inequalities hold simultaneously for different types of well-known convexities as well as for different kinds of fractional integrals. Hence, the presented results provide more generalized forms of the Hadamard type inequalities as compared to the inequalities that already exist in the literature.

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Certain Recurrence Relations of Two Parametric Mittag-Leffler Function and Their Application in Fractional Calculus

Cited by 4 publications

References 38 publications

Certain Integrals of Product of Mittag-Leffler Function, M-Series and I-Function of Two Variables

Certain Integrals of Product of Mittag-Leffler Function, M-Series and I-Function of Two Variables

The Fractional Series Solutions for the Conformable Time‐Fractional Swift‐Hohenberg Equation through the Conformable Shehu Daftardar‐Jafari Approach with Comparative Analysis

Fejér–Hadamard Type Inequalities for (α, h-m)-p-Convex Functions via Extended Generalized Fractional Integrals

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