To Theory One Class Linear Model Noclassical Volterra Type Integral Equation with Left Boundary Singular Point

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In this work, we investigate one class of Volterra type
integral equation, in model case, when kernels have first order fixed
singularity and logarithmic singularity. In detail study the case, when *n* = 3. In depend of the signs parameters solution to this integral
equation can contain three arbitrary constants, two arbitrary constants, one
constant and may have unique solution. In the case when general solution of integral equation
contains arbitrary constants, we stand and investigate
different boundary value problems, when conditions are given in singular point.
Besides for considered integral equation, the solution found cane represented
in generalized power series. Some results obtained in the general model case.

References

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[2] N. Rajabov, “On a Volterra Integral Equation,” Doclady Mathematics, Vol. 65, No. 2, 2002, pp. 217-220.

[3] N. Rajabov, “System of Linear Integral Equations of Volterra Type with Singular and Super-singular Kernels,” Ill-Posed and Non-Classical Problems of Mathematical Physics and Analysis. Proceedings of the International Conference, Samarkand, Uzbekistan, Kluwer, Utrecht, Boston, 11-15 September 2000, pp. 103-124.

[4] N. Rajabov, “About One Class of Volterra Type Linear Integral Equations with an Interior Fixed Singular or Super-singular Point,” Topics in Analysisand its Applications, NATO Science Series, II, Mathematics, Physics and Chemistry, Vol. 147, Kluwer Academic Publishers, 2004, pp. 317-326.

[5] N. Rajabov, “Volterra Type Integral Equation with Boundary and Interior Fixed Singularity and Super-Singularity Kernels and Their Application,” LAPLAMBERT Academic Publishing, 2011, 282 p.

[6] N. Rajabov, “About New Class of Volterra Type Integral Equations with Boundary Singularity in Kernels,” In Advances in Applied Mathematics and Approximation Theory: Contributions from AMAT2012, Springer, 2012, pp. 341-360.

[7] N. Rajabov, “To Theory One Class Modeling Linear Volterra Type Integral Equation with Boundary Singular Kernels,” Theses of Reports of the 4th International Conference “Function Spaces. Differential Operators. General Topology. Problems of Mathematical Education”, PFUR Publishers, Moscow, 2013, pp. 221-222.