Results 11 to 20 of about 56 (56)

On the Kolmogorov forward equations within Caputo and Riemann-Liouville fractions derivatives

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2016
In this work, we focus on the fractional versions of the well-known Kolmogorov forward equations. We consider the problem in two cases. In case 1, we apply the left Caputo fractional derivatives for α ∈ (0, 1] and in case 2, we use the right Riemann ...
Alipour Mohsen, Baleanu Dumitru
doaj   +1 more source

Singularly perturbed Volterra integral equations with weakly singular kernels

International Journal of Mathematics and Mathematical Sciences, Volume 30, Issue 3, Page 129-143, 2002., 2002
We consider finding asymptotic solutions of the singularly perturbed linear Volterra integral equations with weakly singular kernels. An interesting aspect of these problems is that the discontinuity of the kernel causes layer solutions to decay algebraically rather than exponentially within the initial (boundary) layer. To analyse this phenomenon, the
Angelina Bijura
wiley   +1 more source

Fractional calculus containing certain bivariate Mittag-Leffler kernel with respect to function

Demonstratio Mathematica
In the present study, we introduce a general integral operator containing bivariate Mittag-Leffler (M-L) kernel with respect to a function τ(z)\tau \left(z).
Özarslan Mehmet Ali, Kürt Cemaliye
doaj   +1 more source

On Hadamard and Fejér–Hadamard Inequalities for Fractional Integrals Involving Mittag‐Leffler‐Type Function of Arbitrary Order

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
This paper introduces and investigates novel fractional integral operators featuring the extended Mittag‐Leffler function in the kernel. After establishing the core properties of these operators, we derive the corresponding Hadamard and Fejér–Hadamard inequalities.
Maged Bin-Saad, Jihad Younis, Maryam Salem Alatawi, Ali N. A. Koam, Shanhe Wu   +4 more
wiley   +1 more source

A study of generalized Mittag-Leffler-type function of arbitrary order

Demonstratio Mathematica
We present a novel generalized Mittag-Leffler-type function of arbitrary order in this study. We look into its fundamental characteristics, such as differential formulas, recurrence relations, integral representations, the Euler, Laplace, Mellin ...
Bin-Saad Maged, Younis Jihad
doaj   +1 more source

Inverse hyperbolic equation, Spectral technique, Regularization method, Operational matrix

Kuwait Journal of Science
Recently, the realm related to Euler's Beta function has played a significant role in the development of special function theory. In this study, a new extension of the special function known as Euler's Beta function with respect to the Mittag-Leffler ...
Firas Ghanim, Hiba Fawzi Al-Janaby, Marwan Al-Momani   +2 more
doaj   +1 more source

A Family of Hybrid Functions Generated by the Composition of Bessel and Mittag–Leffler Functions

Journal of Mathematics, Volume 2026, Issue 1, 2026.
In this paper, we employ a symbolic technique to introduce a new family of Mittag–Leffler–Bessel functions (MLBFs), formed by compositionally combining the classical Bessel functions of the first kind with the three‐parameter Mittag–Leffler function.
Maged G. Bin-Saad, Waleed K. Mohammed, Guotao Wang   +2 more
wiley   +1 more source

A General Class of Multivariable Mittag–Leffler Function and Its Associated Applications

Abstract and Applied Analysis, Volume 2025, Issue 1, 2025.
In this paper, a new class of multivariable special functions and their generalizations is introduced and used to solve generalized fractional differential and kinetic equations. By applying the Sumudu transform, we derive solutions for the fractional differential equations and fractional kinetic equations expressed in terms of Prabhakar’s Mittag ...
B. B. Jaimini, Meenu, Suman Sharma, S. D. Purohit, D. L. Suthar, Deepali   +5 more
wiley   +1 more source

Application of (q, τ)‐Bernoulli Interpolation to the Spectral Solution of Quantum Differential Equations

International Journal of Differential Equations, Volume 2025, Issue 1, 2025.
In order to solve fractional differential equations on quantum domains, this work provides a spectral approach based on higher‐order (q, τ)‐Bernoulli functions and polynomials. We build a robust basis for approximation in (q, τ)‐weighted Hilbert spaces by using the orthogonality properties of these extended polynomials and the Sheffer‐type generating ...
Shaher Momani, Rabha W. Ibrahim, Khalil Ezzinbi   +2 more
wiley   +1 more source

On the solutions of generalized Cauchy differential equations and diffusion equations with k-Hilfer-Prabhakar derivative

Partial Differential Equations in Applied Mathematics
In this article, natural transform of k-Prabhakar integral, k-Prabhakar derivative, k-Hilfer-Prabhakar fractional derivative (k-HPFD) are calculated. In addition, we also obtain the natural transform of regularized versions of k-Prabhakar integral, k ...
Ved Prakash Dubey, Jagdev Singh, Sarvesh Dubey, Dumitru Baleanu, Devendra Kumar   +4 more
doaj   +1 more source