On a class of coupled fractional nonlinear singular boundary value problems arising in dusty fluid models

Lok Nath Kannaujiya; Narendra Kumar; Amit K. Verma

Home/Archive/arXiv

arXiv · 2507.00017

On a class of coupled fractional nonlinear singular boundary value problems arising in dusty fluid models

Lok Nath Kannaujiya·Narendra Kumar·Amit K. Verma

View original source ↗Read source document ↗Export metadata ↓

Abstract

In this article, we introduce a new class of coupled fractional Lane-Emden boundary value problems. We employ a novel approach, the fractional Haar wavelet collocation method with the Newton-Raphson method. We analyze the conditions in two cases to present numerical experiments related to the defined system of fractional differential equations. To validate the accuracy of the proposed method we present the convergence of the method, and we demonstrate the method's effectiveness through five numerical experiments, highlighting real-world applications of fractional differential equations. Using figures and tables, we show that the residual error decreases as we increase the value of the maximum level of resolution $J$ while keeping the order of derivatives fixed, and similar trends also observe when $J$ is fixed and vary the order of fractional derivatives. We demonstrate that Mathematica software can be used effectively to solve such nonlinear singular fractional boundary value problems.

Explore related subjects

math.GM

Keep this discovery

BibTeX RIS

Lok Nath Kannaujiya, Narendra Kumar, Amit K. Verma. 2025-06-14. On a class of coupled fractional nonlinear singular boundary value problems arising in dusty fluid models. https://arxiv.org/abs/2507.00017

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Average Chord Lengths in a Triangle

Let $P$ be a point inside a triangle $T$. We consider the average length of the chords of $T$ through $P$, where the direction of the chord is chosen uniformly. An elementary formula is obtained in terms of the distances from $P$ to the sides and vertices of the triangle. Several classical triangle centers give especially simple specializations. For example, if $I$ is the incenter, then \[ M_T(I)=\frac{2r}{\pi} \log\left(\cot\frac A4\cot\frac B4\cot\frac C4\right). \] Our main result is the sharp inequality \[ M_T(P)\le \frac{p}{\pi\sqrt3}\log(2+\sqrt3), \] valid simultaneously for every triangle of perimeter $p$ and every interior point $P$. Thus, among all such pairs $(T,P)$, the largest possible average chord length occurs only when $T$ is equilateral and $P$ is its center. The proof is an elementary symmetrization argument. We close with brief remarks relating the problem to the radial center of a convex body, the electrostatic potential center of a triangle, and dual quermassintegrals.

math.GM↗

arXiv2026

The decrease in sectional curvature of the Fisher--Rao manifold of beta distributions

In the paper, the author develops a general convexity lemma and applies it to demonstrate the monotonic decrease of a function involving polygamma functions, arising from the sectional curvature of the Fisher--Rao manifold of beta distributions.

math.GM↗

arXiv2026

A Proof of Liu's Conjecture on the Fundamental Triangle Inequality

Let $a,b,c$ be the side lengths of a triangle, and let $R$ and $r$ denote its circumradius and inradius, respectively. We prove a conjecture of Liu stating that \[\sum_{\mathrm{cyc}} \left(\frac{a(b+c-a)}{bc}\right)^k \geq 2+\left(\frac{2r}{R}\right)^k,~~k>1, \] with the reverse inequality for $0<k<1$. The proof reduces the problem to three positive variables with fixed sum and product. We also determine the equality cases.

math.GM↗