Mohand Transform for Solution of Integral Equations and Abel's Equation

Naresh Parkala, Upender Reddy Gujjula

Abstract: Integral transforms play a crucial role in determining the precise solution to differential equations and are distinguished by their simplicity and convenience. Several academics, beginning with Laplace, have formulated comprehensive equations for integral transforms. These transformations also hold significant importance in discovering precise answers to physical, technical, medicinal, and nuclear challenges, as well as in the fields of astronomy and economics. There are various types of integral transforms like Elzaki, Kamal, Aboodh, Mahgoub, sawi, Rishi, Anuj, Tarig, Kushare, Upadhyaya etc. were discussed about the solution of integral equations of linear volterra integral equations first kind and second kind, convolution type of volterra integral equations also Abel?s integral equations. Here we discussed how the new integral transform Mohand is applicable to solve the integral equations and also convolution type of integral equations for unique solution of first and second kind of volterra integral equations, convolution type integral equations and also discussed Abel?s integral equations.

Keywords: Mohand transform, inverse Mohand transform, linear volterra integral equations (VIE), convolution model of VIE, Abel?s equation, Laplace transform