Saiful R. Mondal

Bio: Saiful R. Mondal is an academic researcher from King Faisal University. The author has contributed to research in topics: Struve function & Bessel function. The author has an hindex of 10, co-authored 46 publications receiving 284 citations. Previous affiliations of Saiful R. Mondal include Indian Institute of Technology Roorkee & Universiti Sains Malaysia.

Geometric Properties of Generalized Bessel Functions

Abstract: In this work, the generalized Bessel functions with their normal- ization are considered. Various conditions are obtained so that these Bessel functions have certain geometric properties including close-to-convexity (univa- lency), starlikeness and convexity in the unit disc. Results obtained for certain classes are new and for the other classes for which similar results exist in the literature, examples are given to support that these results are better than the existing ones.

Marichev-Saigo-Maeda Fractional Integration Operators Involving Generalized Bessel Functions

Abstract: Two integral operators involving Appell's functions, or Horn's function in the kernel are considered. Composition of such functions with generalized Bessel functions of the first kind is expressed in terms of generalized Wright function and generalized hypergeometric series. Many special cases, including cosine and sine function, are also discussed.

On the positivity of certain trigonometric sums and their applications

Abstract: In this paper, we find conditions on the coefficients {b"k}"k"="1^n such that the corresponding trigonometric (cosine and sine) sums given respectively by @?k=1nb"[email protected]>0 and @?k=1nb"[email protected]>0 for all [email protected]?N are positive. Using these results, we find that the functions f that are in the class of analytic functions A are starlike of certain order in the unit disc D by means of conditions on the Taylor coefficients of f. As an application, we also find conditions such that the Cesaro means of order @b of f(z) are close-to-convex and starlike in D.

Certain unified integral formulas involving the generalized modified k-Bessel function of first kind

Abstract: Generalized integral formulas involving the generalized modified k-Bessel function J^{b,c,?,?}_{k,?} (z) of first kind are expressed in terms generalized Wright functions. Some interesting special cases of the main results are also discussed

Geometric Properties of Generalized Bessel Functions

Abstract: The goal of the present chapter is to study some geometric properties (like univalence, starlikeness, convexity, close-to-convexity) of generalized Bessel functions of the first kind. In order to achieve our goal we use several methods: differential subordinations technique, Alexander transform, results of L. Fejer, W. Kaplan, S. Owa and H.M. Srivastava, S. Ozaki, S. Ponnusamy and M. Vuorinen, H. Silverman, and Jack’s lemma. Moreover, we present some immediate applications of univalence and convexity involving generalized Bessel functions associated with the Hardy space and a monotonicity property of generalized and normalized Bessel functions of the first kind.

Sharp bounds for the Toader mean of order 3 in terms of arithmetic, quadratic and contraharmonic means

Abstract: Abstract In the article, we present the best possible parameters α1, β1, α2, β2 ∈ ℝ and α3, β3 ∈ [1/2, 1] such that the double inequalities α1C(a,b)+(1−α1)A(a,b) 0 with a ≠ b, and provide new bounds for the complete elliptic integral of the second kind, where A(a, b) = (a + b)/2 is the arithmetic mean, Q(a,b)=a2+b2/2 $\\begin{array}{} \\displaystyle Q(a, b)=\\sqrt{\\left(a^{2}+b^{2}\\right)/2} \\end{array}$ is the quadratic mean, C(a, b) = (a2 + b2)/(a + b) is the contra-harmonic mean, C(p; a, b) = C[pa + (1 – p)b, pb + (1 – p)a] is the one-parameter contra-harmonic mean and T3(a,b)=(2π∫0π/2a3cos2⁡θ+b3sin2⁡θdθ)2/3 $\\begin{array}{} T_{3}(a,b)=\\Big(\\frac{2}{\\pi}\\int\\limits_{0}^{\\pi/2}\\sqrt{a^{3}\\cos^{2}\\theta+b^{3}\\sin^{2}\\theta}\\text{d}\\theta\\Big)^{2/3} \\end{array}$ is the Toader mean of order 3.

Analysis of reaction–diffusion system via a new fractional derivative with non-singular kernel

Abstract: In this paper, we obtain analytical solutions for the fractional cubic isothermal auto-catalytic chemical system with Caputo–Fabrizio and Atangana–Baleanu fractional time derivatives in Liouville–Caputo sense. We utilize the q-homotopy analysis transform method to compute the approximate solutions. We find the optimal values of h so we assure the convergence of the approximate solutions. Finally, we compare our results numerically with the finite difference method and excellent agreement is found.

Starlikeness and convexity of generalized Bessel functions

Abstract: In this paper, we give sufficient conditions for the parameters of the normalized form of the generalized Bessel functions to be convex and starlike in the open unit disk. As an application of our main results, we solve a recent open problem concerning a subordination property of Bessel functions with different parameters. Moreover, we present a new inequality for the Euler gamma function, which we apply in order to have tight bounds for the generalized and normalized Bessel function of the first kind.