The object of the present work is to deduce several important developments in various recursion relations, relevant differential recursion formulas, infinite summation formulas, integral representations, and integral operators for Horn’s hypergeometric functions ?1 and ?2.

In this paper, we establish some fixed point results for αqsp -admissible mappings embedded in L-simulation functions in the context of b-metric-like spaces. As an application, we discuss the existence of a unique solution for fractional hybrid differential  equation with multipoint boundary conditions via Caputo fractional derivative of order 1 < α ≤ 2. Some examples and corollaries are also considered to illustrate the obtained results.

The object of the present work is to deduce several important developments in various recursion relations, relevant differential
recursion formulas, infinite summation formulas, integral representations, and integral operators for Horn’s hypergeometric
functions ?1 and ?2.

In this paper, we establish some fixed point results for αqsp -admissible mappings embedded in L-simulation functions in the
context of b-metric-like spaces. As an application, we discuss the existence of a unique solution for fractional hybrid differential
equation with multipoint boundary conditions via Caputo fractional derivative of order 1 < α ≤ 2. Some examples and corollaries
are also considered to illustrate the obtained results.

The purpose of this work is to demonstrate several interesting contiguous function
relations and q-differential formulas for basic Horn hypergeometric functions H3 and
H4. Some properties of our main results are also constructed.

Motivated by recent investigations, the main object of this paper is to construct the new
(p, q)-analogy definitions of the various families of (p, q)-Bessel functions using the generating
function method as a starting point. We derive the explicit representations, especially
differential recurrence relations and these classes results of the (p, q)-Bessel functions.

The main object of the present paper is to construct new (p, q)-analogy definitions of various families of (p, q)-Humbert functions using the generating function method as a starting point. This study shows a class of several results of (p, q)-Humbert functions with the help of the generating functions such as explicit representations and recurrence relations, especially differential recurrence relations, and prove some of their significant properties of these functions.