On the Boundary Value Problem of Nonlinear Fractional Integro-Differential Equations

Li, Chenkuan; Saadati, Reza; Srivastava, Rekha; Beaudin, Joshua

doi:10.3390/math10121971

Cited by 7 publications

(1 citation statement)

References 20 publications

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“…s (s, x)ds, 0 < α ≤ 1. * Correspondence: lic@brandonu.ca, rsaadati@eml.cc From [2,3], we have for 0 < α ≤ 1 , (I 0 t u)(t, x) = u(t, x),…”

Section: Backgroundsmentioning

confidence: 99%

Remarks on a fractional nonlinear partial integro-differential equation via the new generalized multivariate Mittag-Leffler function *

Saadati

Beaudin

et al. 2023

Preprint

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Introducing the new generalized multivariate Mittag-Leffler function, we consider the uniqueness of solutions to a boundary value problem of the fractional nonlinear partial integro-differential equation using Banach’s fixed point theorem and Babenko’s technique. In addition, we use Python which is a high-level language efficiently dealing with the summation of multi indices to compute the approximate value of the generalized Mittag-Leffler function, and provide an example showing applications of key results derived. Mathematics Subject Classification: 65M25, 65Q30, 35C10, 35C15, 26A33

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“…s (s, x)ds, 0 < α ≤ 1. * Correspondence: lic@brandonu.ca, rsaadati@eml.cc From [2,3], we have for 0 < α ≤ 1 , (I 0 t u)(t, x) = u(t, x),…”

Section: Backgroundsmentioning

confidence: 99%

Remarks on a fractional nonlinear partial integro-differential equation via the new generalized multivariate Mittag-Leffler function *

Saadati

Beaudin

et al. 2023

Preprint

Self Cite

View full text Add to dashboard Cite

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Some results on a nonlinear fractional equation with nonlocal boundary condition

Li,

Saadati,

Beaudin

et al. 2024

Math Methods in App Sciences

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The aim of this paper is to derive sufficient conditions for the existence, uniqueness, and Hyers–Ulam stability of solutions to a new nonlinear fractional integro‐differential equation with functional boundary conditions, using several fixed‐point theorems, the multivariate Mittag‐Leffler function and Babenko's approach. A few examples are also presented to illustrate the applications of our results based on approximate values of a couple of Mittag‐Leffler functions calculated by Python codes. Furthermore, the approaches used have a wide range of applications to various fractional differential equations with initial or boundary conditions or integral equations in complete spaces.

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The Matrix Mittag–Leffler Function and Nonlinear Fractional Integro–Differential Equations

Rezaei Aderyani,

Saadati,

et al. 2024

Studies in Systems, Decision and Control

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On the Boundary Value Problem of Nonlinear Fractional Integro-Differential Equations

Cited by 7 publications

References 20 publications

Remarks on a fractional nonlinear partial integro-differential equation via the new generalized multivariate Mittag-Leffler function *

Remarks on a fractional nonlinear partial integro-differential equation via the new generalized multivariate Mittag-Leffler function *

Some results on a nonlinear fractional equation with nonlocal boundary condition

The Matrix Mittag–Leffler Function and Nonlinear Fractional Integro–Differential Equations

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