IHJPAS. 36(1)2023 

400 
 This work is licensed under a Creative Commons Attribution 4.0 International License 

 

   

 

 

Using a New General Complex Integral Transform for Solving Population 

Growth and Decay Problems  

 

 

 
 

 

 

Abstract  

The Population growth and decay issues are one of the most pressing issues in many sectors 

of study. These issues can be found in physics, chemistry, social science, biology, and zoology, 

among other subjects . 

We introduced the solution for these problems in this paper by using the SEJI (Sadiq- Emad- Jinan) 

integral transform, which has some mathematical properties that we use in our solutions. We also 

presented the SEJI transform for some functions, followed by the inverse of the SEJI integral 

transform for these functions. 

After that, we demonstrate how to use the SEJI transform to tackle population growth and decay 

problems by presenting two applications that demonstrate how to use this transform to obtain 

solutions . 

Finally, we conclude that the SEJI transform can readily solve the problems of population 

increase and decay, and that the action of this integral transform in overcoming these challenges 

can be explained through applications. 

Keywords: decay problems, inverse of SEJI transform, population growth, SEJI transform. 

1. Introduction: 

There are many integral transforms have been solved the population growth and decay 

problems, such as Sawi, Mohand, Kamal, Shehu, Elzaki and complex SEE transform [1-7]. 

The equation of population growth is a first order linear ordinary differential equation [8-12].  

                               
𝑑𝑁

𝑑𝑡
= 𝜇𝑁.                                                                                                     (1) 

With initial condition  

doi.org/10.30526/36.1.2882 

Article history: Received 21 June 2022, Accepted 21 Augest 2022, Published in January 2023. 

 

 

 

Ibn Al-Haitham Journal for Pure and Applied Sciences 

Journal homepage: jih.uobaghdad.edu.iq 

 

Sadiq A. Mehdi 

Department of Mathematics, College 

of Education, Mustansiriyah 

University, Baghdad, Iraq 

Sadiqmehdi71@uomustansiriyah.edu.iq 

Emad A. Kuffi 

Department of Materials, College of 

Engineering, Al-Qadisiyah 

University, Al-Qadisiyah, Iraq.  
emad.abbas@qu.edu.iq 

 

 
 

Jinan A. Jasim 

Department of Mathematics, College 

of Education, Mustansiriyah 

University, Baghdad, Iraq 

jinanadel78@uomustansiriyah.edu.iq  

https://creativecommons.org/licenses/by/4.0/
mailto:Sadiqmehdi71@uomustansiriyah.edu.iq
mailto:emad.abbas@qu.edu.iq
mailto:jinanadel78@uomustansiriyah.edu.iq


IHJPAS. 36(1)2023 
 

401 
 

                              𝑁(𝑡0) = 𝑁0.                                                                                        (2) 

 Where 𝜇 is a positive real number, 𝑁 is the population value at time 𝑡 and 𝑁0  is the initial 

population at time 𝑡0 . 

 This equation is known as the Malthusian law of population growth. 

 The decay problems of the core are defined as first order linear ordinary differential 

equations [13-15]. 

                              
𝑑𝑀

𝑑𝑡
= −𝜂𝑀.                                                                                                (3) 

With initial condition  

                              𝑀(𝑡0) = 𝑀0.                                                                                                (4) 

Where  𝑀 is the value of the matter at time 𝑡, 𝜂 ∈ ℝ+ and 𝑀0 is the initial matter at time 𝑡0. 

 The negative sign in the equation (3) points the mass of the core decreases with time, thus 

the time derivative of 𝑀 denoted by 
𝑑𝑀

𝑑𝑡
  have to be negative. 

 We define the SEJI integral transform as follows [16]: 

𝑇𝑔
𝑐 {𝑓(𝑡); 𝑠} = 𝐹𝑔

𝑐 (𝑠) = 𝑝(𝑠) ∫ 𝑒−𝑖𝑞(𝑠)𝑡 𝑓(𝑡)𝑑𝑡,
∞

𝑡=0

 

where 𝑡 ≥ 0, 𝑝(𝑠) ≠ 0 and 𝑞(𝑠) are positive functions of parameter 𝑠, 𝑖 = √−1. 

 The SEJI integral transform of the function 𝑓(𝑡), 𝑡 ≥ 0 has a condition that 𝑓(𝑡) is a 

piecewise continuous and 𝑓(𝑡) of exponential order, which these sufficient conditions for the 

existence of SEJI integral transform for 𝑓(𝑡). 

2. The Linearity Property of SEJE Transform 

 We can prove easily the linearity property of the SEJE transform. 

Let 𝑇𝑔
𝑐 {𝑓(𝑡)} = 𝐹𝑔

𝑐 (𝑠) and 𝑇𝑔
𝑐 {ℎ(𝑡)} = 𝐻𝑔

𝑐 (𝑠), then for every 𝛼 and 𝛽 are constants 

𝑇𝑔
𝑐 {𝛼𝑓(𝑡) ± 𝛽ℎ(𝑡)} = 𝛼𝐹𝑔

𝑐 (𝑠) ± 𝛽𝐻𝑔
𝑐 (𝑠) 

Proof: 

𝑇𝑔
𝑐 {𝛼𝑓(𝑡) ± 𝛽ℎ(𝑡)} = 𝑝(𝑠) ∫ 𝑒−𝑖𝑞(𝑠)𝑡 (𝛼𝑓(𝑡) ± 𝛽ℎ(𝑡))𝑑𝑡,                                             

∞

𝑡=0

 

                                = 𝑝(𝑠) ∫ 𝑒−𝑖𝑞(𝑠)𝑡 (𝛼𝑓(𝑡))𝑑𝑡 ± 𝑝(𝑠) ∫ 𝑒−𝑖𝑞(𝑠)𝑡 (𝛽ℎ(𝑡))𝑑𝑡,
∞

𝑡=0

  
∞

𝑡=0

 

                             = 𝛼𝑝(𝑠) ∫ 𝑒−𝑖𝑞(𝑠)𝑡 𝑓(𝑡)𝑑𝑡 ± 𝛽𝑝(𝑠) ∫ 𝑒−𝑖𝑞(𝑠)𝑡 ℎ(𝑡)𝑑𝑡,
∞

𝑡=0

          
∞

𝑡=0

 

   = 𝛼𝐹𝑔
𝑐 (𝑠) ± 𝛽𝐻𝑔

𝑐 (𝑠).           ∎                                       

 Also, we can prove this property for the inverse of SEJI integral transform. 

𝑓(𝑡) = 𝑇𝑔
𝑐 −1{𝐹𝑔

𝑐 (𝑠)} =
1

2𝜋𝑖
∫

𝑖

𝑝(𝑠)
𝑒𝑖𝑞(𝑠)𝑡 𝐹𝑔

𝑐 (𝑠)𝑑𝑠,        
𝛿+𝑖∞

𝛿−𝑖∞

 

where 𝛿 is positive fixed number, 𝑡 ≥ 0. 𝑖 is complex number (𝑖2 = −1). 

Let 𝑇𝑔
𝑐 −1{𝐹𝑔

𝑐 (𝑠)} = 𝑓(𝑡) and 𝑇𝑔
𝑐 −1{𝐻𝑔

𝑐 (𝑠)} = ℎ(𝑡) then for every 𝛼 and 𝛽 are constant 



IHJPAS. 36(1)2023 
 

402 
 

𝑇𝑔
𝑐 −1{𝛼𝐹𝑔

𝑐 (𝑠) ± 𝛽𝐻𝑔
𝑐 (𝑠)} = 𝛼𝑓(𝑡) ± 𝛽ℎ(𝑡)  . 

Proof: 

𝑇𝑔
𝑐 −1{𝛼𝐹𝑔

𝑐 (𝑠) ± 𝛽𝐻𝑔
𝑐 (𝑠)} =

1

2𝜋𝑖
∫

𝑖

𝑝(𝑠)
𝑒𝑖𝑞(𝑠)𝑡 (𝛼𝐹𝑔

𝑐 (𝑠) ± 𝛽𝐻𝑔
𝑐 (𝑠)) 𝑑𝑠,           

𝛿+𝑖∞

𝛿−𝑖∞

 

=
1

2𝜋𝑖
∫

𝑖

𝑝(𝑠)
𝑒 𝑖𝑞(𝑠)𝑡 (𝛼𝐹𝑔

𝑐 (𝑠)) 𝑑𝑠 ±
1

2𝜋𝑖
∫

𝑖

𝑝(𝑠)
𝑒𝑖𝑞(𝑠)𝑡 (𝛽𝐻𝑔

𝑐 (𝑠)) 𝑑𝑠,        
𝛿+𝑖∞

𝛿−𝑖∞

 
𝛿+𝑖∞

𝛿−𝑖∞

 

=
𝛼

2𝜋𝑖
∫

𝑖

𝑝(𝑠)
𝑒 𝑖𝑞(𝑠)𝑡 𝐹𝑔

𝑐 (𝑠)𝑑𝑠 ±
𝛽

2𝜋𝑖
∫

𝑖

𝑝(𝑠)
𝑒𝑖𝑞(𝑠)𝑡 𝐻𝑔

𝑐 (𝑠)𝑑𝑠,                  
𝛿+𝑖∞

𝛿−𝑖∞

        
𝛿+𝑖∞

𝛿−𝑖∞

 

= 𝛼𝑓(𝑡) ± 𝛽ℎ(𝑡).     ∎                                                                                                    

3. The SEJI Integral Transform for Some Fundamental Functions: [16] 

In the following a list the SEJE transform for some important functions: 

Table 1. The SEJE transform for some basic functions. 

Functions 𝒇(𝒕) 𝑻𝒈
𝒄 {𝒇(𝒕)} = 𝑭𝒈

𝒄 (𝒔) Functions 

𝒇(𝒕) 

𝑻𝒈
𝒄 {𝒇(𝒕)} = 𝑭𝒈

𝒄 (𝒔) 

1.   1 −𝑖𝑝(𝑠)

𝑞(𝑠)
 

6. 𝑒 𝛼𝑡 ,   𝛼 is a 

constant −𝑝(𝑠) [
𝛼  

𝛼 2 + (𝑞(𝑠))
2

+ 𝑖
𝑞(𝑠)

𝛼 2 + (𝑞(𝑠))
2

] ,   𝑞(𝑠) > 𝑎. 

2.   t −  𝑝(𝑠)

[𝑞(𝑠)]2
 

7. sin(𝛼𝑡) −𝛼 𝑝(𝑠) 

(𝑞(𝑠))
2

− 𝛼 2
,   𝑞(𝑠) > |𝛼| 

3.  𝑡 2 2𝑖𝑝(𝑠)

[𝑞(𝑠)]3
 

8. cos(𝛼𝑡) −𝑖 𝑝(𝑠) 𝑞(𝑠)

(𝑞(𝑠))
2

− 𝛼 2
,    𝑞(𝑠) > |𝛼|. 

4.   𝑡 𝑛,    𝑛 ∈ 𝑁 
(−𝑖)𝑛+1

𝑛!   𝑝(𝑠)

[𝑞(𝑠)]𝑛+1
 

9. sinh(𝛼𝑡) −𝛼 𝑝(𝑠) 

(𝑞(𝑠))
2

+ 𝛼 2
 ,    𝑞(𝑠) > 0. 

5.   𝑡 𝑛, 𝑛 > −1 
(−𝑖)𝑛+1

Γ(𝑛 + 1)  𝑝(𝑠)

[𝑞(𝑠)]𝑛+1
 

10. cosh(𝛼𝑡) −𝑖 𝑝(𝑠) 𝑞(𝑠)

(𝑞(𝑠))
2

+ 𝛼 2
,         𝑞(𝑠) > 0. 

 

4. The Inverse of SEJI Integral Transform for Some Fundamental Functions: [16] 

 In the following a list of the inverse of the SEJI integral transform for some important 

functions: 

 

 

 

 

 

Table 2. The inverse of SEJE transform for some basic functions. 



IHJPAS. 36(1)2023 
 

403 
 

𝑭𝒈
𝒄 (𝒔) 𝒇(𝒕) = 𝑻𝒈

𝒄 −𝟏{𝑭𝒈
𝒄 (𝒔)} 𝑭𝒈

𝒄 (𝒔) 𝒇(𝒕) = 𝑻𝒈
𝒄 −𝟏{𝑭𝒈

𝒄 (𝒔)} 

1.  
−𝑖𝑝(𝑠)

𝑞(𝑠)
 1 6. −𝑝(𝑠) [

𝛽  

𝛽2+(𝑞(𝑠))
2 +

𝑖
𝑞(𝑠)

𝛽2+(𝑞(𝑠))
2],   

 𝑞(𝑠) > 𝛽. 

𝑒 𝛽𝑡 ,   𝛽 is a constant 

2. 
−  𝑝(𝑠)

[𝑞(𝑠)]2
 t 7. 

−𝛽 𝑝(𝑠) 

(𝑞(𝑠))
2

−𝛽2
,   

 𝑞(𝑠) > |𝛽| 

sin(𝛽𝑡) 

3. 
2𝑖𝑝(𝑠)

[𝑞(𝑠)]3
 𝑡

2

2!
 

8. 
−𝑖 𝑝(𝑠) 𝑞(𝑠)

(𝑞(𝑠))
2

−𝛽2
, 

    𝑞(𝑠) > |𝛽|. 

cos(𝛽𝑡) 

4. (−𝑖)𝑛+1
𝑝(𝑠)

[𝑞(𝑠)]𝑛+1
, 

 𝑛 ∈ 𝑁 

𝑡 𝑛

𝑛!
 9. 

−𝛽 𝑝(𝑠) 

(𝑞(𝑠))
2

+𝛽2
 ,  

   𝑞(𝑠) > 0. 

sinh(𝛽𝑡) 

5. (−𝑖)𝑛+1
  𝑝(𝑠)

[𝑞(𝑠)]𝑛+1
, 

 𝑛 > −1 

𝑡 𝑛

Γ(𝑛 + 1)
 10. 

−𝑖 𝑝(𝑠) 𝑞(𝑠)

(𝑞(𝑠))
2

+𝛽2
,    

      𝑞(𝑠) > 0. 

cosh(𝛽𝑡) 

 

 

5.The SEJI Integral Transform of Derivatives of a Function 𝐟(𝐭):  [16] 

In [10] gave the application of SEJI integral transform to derivative of 𝑓(𝑡). 

Let 𝑇𝑔
𝑐 {𝑓(𝑡)} = 𝐹𝑔

𝑐 (𝑠), we get: 

i. 𝑇𝑔
𝑐 {𝑓′(𝑡)} = 𝑖𝑞(𝑠)𝐹𝑔

𝑐 (𝑠) − 𝑓(0)𝑝(𝑠).                                                   

ii. 𝑇𝑔
𝑐 {𝑓′′(𝑡)} = (𝑖𝑞(𝑠))

2
𝐹𝑔

𝑐 (𝑠) − 𝑝(𝑠)𝑓 ′(0) − 𝑖𝑞(𝑠)𝑝(𝑠)𝑓(0).      

iii. 𝑇𝑔
𝑐 {𝑓 (𝑛)(𝑡)} = (𝑖𝑞(𝑠))

𝑛
𝐹𝑔

𝑐 (𝑠) − 𝑝(𝑠) [∑ (𝑖𝑞(𝑠))
𝑘−1𝑛

𝑘=1 𝑓
(𝑛−𝑘)(0)]. 

 

6.The Method of SEJI Integral Transform for Solving The Population Growth Problem: 

 In this section, we illustrate the method of solution the population growth problem in equation 

(1) and (2) by using the SEJI integral transform. 

Take the SEJI integral transform for equation (1): 

                              𝑇𝑔
𝑐 {

𝑑𝑁

𝑑𝑡
} = 𝑇𝑔

𝑐 {𝜇𝑁}.                                                                                             (5) 

 As we know, SEJE transform of derivative of function, so we get: 

                             𝑖𝑞(𝑠)𝑁𝑔
𝑐 (𝑠) − 𝑁(0)𝑝(𝑠) = 𝜇𝑁𝑔

𝑐 (𝑠).                                                                        (6)  

 By applying the initial condition (2) and on simplification, we get: 

                    𝑁𝑔
𝑐 (𝑠)[𝑖𝑞(𝑠) − 𝜇] = 𝑁0𝑝(𝑠).                                                                         

Then, 

                              𝑁𝑔
𝑐 (𝑠) =

𝑁0𝑝(𝑠)

[𝑖𝑞(𝑠) − 𝜇]
.                                                                                                (7) 

 For obtaining the value of 𝑁(𝑡) we take the inverse SEJE integral transform on both sides of 

(7), so we have: 

                                     𝑁(𝑡) = 𝑇𝑔
𝑐 −1{𝑁𝑔

𝑐 (𝑠)} = 𝑁0 𝑇𝑔
𝑐 −1 {

𝑝(𝑠)

[𝑖𝑞(𝑠) − 𝜇]
},    

𝑁(𝑡) = 𝑁0𝑒
𝜇𝑡 .   ∀t ≥ 0                

where 𝑁(𝑡) be the value of population at time 𝑡. 



IHJPAS. 36(1)2023 
 

404 
 

7.The Method of SEJE Transform for Solving The Decay Problem: 

 In this section, we introduce the method of solution the decay problem in equations (3) and 

(4) by using the SEJE transform. 

 Take the SEJE transform for equation (3): 

                            𝑇𝑔
𝑐 {

𝑑𝑀

𝑑𝑡
} = 𝑇𝑔

𝑐 {−𝜂𝑀}.                                                                                 (8) 

 As we know, SEJE transform of derivative of function, so we have: 

                               𝑖𝑞(𝑠)𝑀𝑔
𝑐 (𝑠) − 𝑀(0)𝑝(𝑠) = −𝜂𝑀𝑔

𝑐 (𝑠).                                                             (9)  

 By applying the initial condition (4) and on simplification, we get: 

                   𝑀𝑔
𝑐 (𝑠)[𝑖𝑞(𝑠) + 𝜂] = 𝑀0𝑝(𝑠),                                                          

we obtain: 

                              𝑀𝑔
𝑐 (𝑠) =

𝑀0𝑝(𝑠)

[𝑖𝑞(𝑠) + 𝜂]
.                                                                                          (10)  

 For obtaining the value of 𝑀(𝑡) we take the inverse SEJE transform on both sides of (10), 

so we have: 

                              𝑀(𝑡) = 𝑇𝑔
𝑐 −1{𝑀𝑔

𝑐 (𝑠)} = 𝑀0 𝑇𝑔
𝑐 −1 {

𝑝(𝑠)

[𝑖𝑞(𝑠) + 𝜂]
},        

𝑀(𝑡) = 𝑀0𝑒
−𝜂𝑡 .   ∀t ≥ 0                

Where 𝑀(𝑡) is the value of substance at time 𝑡. 

8.Applications: 

 We have now some applications to explain the effect of SRJE integral transform in solving 

population growth and decay problems. 

Application 8.1: 

 A country's population expands at a rate proportional to the number of people currently 

residing there. If the population doubles in three years and reaches 10,000 in five years, calculate the 

number of individuals who lived in the country at the start [10]. 

 We can write this information by the following equation: 

                                                                        
𝑑𝑁

𝑑𝑡
= 𝜇𝑁.                                                     (11) 

Where 𝑁 is the number of people living in the country at time 𝑡 and 𝜇 is a proportionality rate. 

Assume that 𝑁0 is the country's initial population at time 𝑡 = 0. 

 Now, we will apply the same steps in equation (11),  

                                                                       𝑇𝑔
𝑐 {

𝑑𝑁

𝑑𝑡
} = 𝜇𝑇𝑔

𝑐 {𝑁}.                                                   (12) 

Since 𝑁 = 𝑁0 when 𝑡 = 0, so we get: 

                                                                   𝑁𝑔
𝑐 (𝑠) =

𝑁0𝑝(𝑠)

[𝑖𝑞(𝑠) − 𝜇]
.                                        (13) 

 By applying inverse of SEJE transform for (13), 

   𝑁(𝑡) = 𝑇𝑔
𝑐 −1{𝑁𝑔

𝑐 (𝑠)} = 𝑁0 𝑇𝑔
𝑐 −1 {

𝑝(𝑠)

[𝑖𝑞(𝑠) − 𝜇]
},    

                                                                       𝑁(𝑡) = 𝑁0𝑒
𝜇𝑡 .                                                    (14) 

 At time 𝑡 = 3, 𝑁 = 2𝑁0, by using in (14), we find: 

2𝑁0 = 𝑁0𝑒
3𝜇 ⇒ 𝑒3𝜇 = 2 



IHJPAS. 36(1)2023 
 

405 
 

𝜇 = 0.231. 

 Now at time 𝑡 = 5, N = 104, using in (14), we get: 

104 = 𝑁0𝑒
3(0.231), 

𝑁0 = 3151. 

Where 𝑁0 is the desired initial value of people living in the country. 

Application 8.2: 

 If there is originally 100 mg. of radioactive material present and after three hours it is noticed 

that the radioactive material has lost 20% of its original mass, calculate the half-life of the radioactive 

substance [10] . 

 We write these information by the following equation: 

                                                                       
𝑑𝑀

𝑑𝑡
= −𝜂𝑀,                                                       (15) 

where 𝜂 is the rate of proportionality and 𝑀 represents the value of radioactive material at time. 

Assume that at time 𝑡 = 0 and 𝑀0is the initial value of p radioactive material. 

 Now, we will apply the same steps in equation (15),  

                                                                       𝑇𝑔
𝑐 {

𝑑𝑀

𝑑𝑡
} = −𝜂𝑇𝑔

𝑐 {𝑀}.                                               (16) 

 Since 𝑀 = 𝑀0 when 𝑡 = 0, so we get: 

                                                                       𝑀𝑔
𝑐 (𝑠) =

𝑀0𝑝(𝑠)

[𝑖𝑞(𝑠) + 𝜂]
.                                               (17) 

 By applying inverse of SEJE integral transform for (17), 

   𝑀(𝑡) = 𝑇𝑔
𝑐 −1{𝑀𝑔

𝑐 (𝑠)} = 𝑀0 𝑇𝑔
𝑐 −1 {

𝑝(𝑠)

[𝑖𝑞(𝑠) + 𝜂]
},    

                                                                        𝑀(𝑡) = 𝑀0𝑒
−𝜂𝑡 .                                                       (18) 

 At time 𝑡 = 0, 𝑀 = 𝑀0 = 100, by using in (8.8), we find: 

                                                                       𝑀(t) = 100𝑒𝜂𝑡 .                                                       (19) 

 Now at time t = 5,  the radioactive material has lost 20 present of its original mass 100 mg. 

therefore,  

𝑀 = 100 − 20 = 80 is using in (18), we get: 

80 = 100𝑒−3𝜂 , 

                                                                       𝜂 = 0.07438.                                                       (20) 

we wanted 𝑡 when 𝑀 =
𝑀0

2
= 50, then from (19), we get: 

                                                                       50 = 100𝑒−𝜂𝑡 .                                                        (21) 

 By substituting the value of 𝜂 in (21),  

50 = 100𝑒−0.07438𝑡 ⇒ 𝑡 = 9.32  hours, 

which t is the desired half-life of the radioactive material. 

 

9.Conclusion 

     In this study, we show how to improve the SEJI integral transform approach for solving 

population growth and decay problems. The effect of the SEJI integral transform for tackling these 

difficulties is explained through the applications. So, we can use the suggested transform to solve 

the population growth and decay problems for the different organisms. 

References 



IHJPAS. 36(1)2023 
 

406 
 

1. Singh, G.P. ; Aggarwal, S. Sawi Transform for Population Growth and Decay Problems. 

International Journal of Latest Technology in Engineering, Management & Applied Science, 

2019, 8(8). 

2. Aggarwal, S.; Sharma, S. D.  Solution of Population Growth and Decay Problems Using 

Smudu Transform, International Journal of Research and Innovation Applied Scence (IJRIAS) 

(2020), Vol.V, Issue VII, July  

3. Aggarwal, S. ; Sharma, N. ; Chauhan, R.  Solution of Population Growth and Decay Problems 

by Using Mohand Transform. International Journal of Research in Advent Technology, 2018, 

6(11), 3277-3282.  

4. Aggarwal , S. ; Gupta, A.R.; Asthana, N. ; Singh, D.P. Application of Kamal Transform for 

Solving Population Growth and Decay Problems. Global Journal of Engineering Science and 

Researches, 2018 ,5(9), 254-260.  

5. Aggarwal, S. ; Sharma, S.D. ; Gupta, A.R.  Application of Shehu Transform for Handling 

Growth and Decay Problems. Global Journal of Engineering Science and Researches, 2019,6(4), 

190-198.    

6. Aggarwal, S.; Singh, D. P. ; Asthana, N. ; Gupta, A.R.  Application of Elzaki Transform for 

Solving Population Growth and Decay Problems. Journal of Emerging Technologies and 

Innovative Research, 2018,5(9), 281-284,  

7. Eman A. Mansour, Emad A. Kuffi ; Sadiq A. Mehdi, Solving Population Growth and Decay 

Problems Using Complex SEE Transform, 7th International Conference on Contemporary 

Information Technology and Mathematics (ICCITM-2021), Mosul, Iraq. 

8.Ahsan, Z., Differential Equations and Their Applications, PHI, 2006.  

9.Ang, W.T. ; Park, Y.S.: Ordinary Differential Equations: Methods and Applications, Universal 

Publishers, 2008 . 

10.Bronson, R. ; Costa, G.B.: Schaum’s Outline of Differential Equations, McGraw-Hill, 2021.   

11.Weigelhofer, W.S. ; Lindsay, K.A.: Ordinary Differential Equations & Applications: 

Mathematical Methods for Applied Mathematicians, Physicists, Engineers and Bioscientists, 

Woodhead, 1999.   

12.Zill, D.G. ; Cullen, M.R., Differential Equations with Boundary Value Problems, Thomson 

Brooks/ Cole, 1996. 

13.Gorain, G.C., Introductory Course on Differential Equations, Narosa, 2014.   

14.Kapur, J.N., Mathematical Modelling, New-Age, 2005.   

15.Roberts, C., Ordinary Differential Equations: Applications, Models and Computing, Chapman 

and Hall/ CRC, 2010.    

16.Sadiq A. Mehdi, Emad A. Kuffi ; Jinan A. Jasim, Solving Ordinary Differential Equations 

Using a New General Complex Integral Transform,  Journal of interdisciplinary mathematics, 

DOI:10.1080/09720502.2022.2089381, 2022.